11th Maths Monthly Test - 1(Two Dimensional Analytical Geometry)

St. Britto Hr. Sec. School - Madurai

11th Maths Monthly Test - 1(Two Dimensional Analytical Geometry)-Aug 2020

Time : 2.30 Hours

Part - A

Multiple Choice Question - Answer All Question

Slope of X-axis or a line parallel to X-axis is

0
positive
negative
infinity

The equation of the straight line upon which the length of perpendicular from the origin is p and this normal makes an angle \(\theta\) with the positive direction of x-axis is

x sin\(\theta\)+ycot\(\theta\)=p
xsin\(\theta\)+ycos\(\theta\)=p
xsin\(\theta\)+ytan\(\theta\)cos\(\theta\)=p
xcos\(\theta\)+ysin\(\theta\)=p

The gradient of one of the lines of ax²+2hxy+by²=0 is twice that of the other, then

h²=ab
h=a+b
8h²=9ab
9h²=8ab

If the equation of the base opposite to the vertex (2,3) of an equilateral triangle is x +y = 2, then the length of a side is

\(\sqrt{\frac{3}{2}}\)
6
\(\sqrt{6}\)
\(3\sqrt{2}\)

Find the point of intersection of the lines 2x²+ xy -y²- 5x + 3y + 2 = 0:

(-1, -1)
(1, 1)
(1, 0)
(0, 1)

The distance between the line 12x - 5y + 9 = 0 and the point (2, 1) is

\(\pm\frac{28}{13}\)
\(\frac{28}{13}\)
\(-\frac{28}{13}\)
none of these

The equation of a line which is equidistant from the lines x=-2 and x=6 is

x=4
x=2
x=3
none of these

The point (2,1) and (-3,5) are on

Same side of the line 3x-2y+1=0
Opposite sides of the line 3x-2y+1=0
On the line 3x-2y+1=0
On the line x+y=3

The distance between the parallel lines 3x-4y+9=0 and 6x-8y-15=0 is

\(\frac{-33}{10}\)
\(\frac{10}{33}\)
\(\frac{33}{10}\)
\(\frac{33}{20}\)

If the points (a, 0) (0, b) and (x,y) are collinear, then

\(\frac{x}{a}-\frac{y}{b}=1\)
\(\frac{x}{a}+\frac{y}{b}=1\)
\(\frac{x}{a}+\frac{y}{b}=-1\)
\(\frac{x}{a}+\frac{y}{b}=0\)

Part - B

Generic 2 - Answer All Question

Find the acute angle between the pair of lines given by 2x²-5xy-7y² = 0.
Show that x² - y² + x - 3y - 2 = 0 represents a pair of straight lines. Find also angle between the lines.

Find the values of k for which the line (k-3)x-(4-k²)y+(k²-7k+6)=0 passes through the origin.

If \(\theta\) is the parameter, find the equation of the locus of a moving point, whose co-ordinates are x=a cos³\(\theta\) ; y = without³\(\theta\) .

Find the combined equation of the straight lines through the origin one of which is parallel to and the other is perpendicular to the straight line 3x + y + 5 = 0.

The sum of the squares of the distances of a moving point from two fixed points (a, 0) and (-0, 0) is equal to 2c². Find the equation to its locus.

Find the combined equation of straight lines whose separate equations are x-2y-3=0 and x+y+5=0.

A straight line is drawn through the point p(2, 3) and is inclined at an angle of 30° with x-axis. Find the co-ordinates of two points on it at a distance of 4 from P on either side of P.

Find the equation of the line through the intersection of lines 3x+4y=7 and x-y+2=0 and whose slope is 5

Find the angle between the pair of straight lines given by
(a² - 3b²)x² + 8ab xy+(b² -3a²)y² =0.

Part - C

Generic 3 - Answer All Question

Find the path traced out by the point \((ct,\frac{c}{t})\) , here t≠0 is the parameter and c is a constant.

Find the equation of the straight line which passes through the point (1, -2) and cuts off equal intercepts from axes.

Find the equation of the perpendicular bisector of the line segment joining the points A(2, 3) and B(6, -5).

Find the equation of a line with slope 2 and the length of the perpendicular from the origin is equal to \(\sqrt{5}\) .
A student when walks from his house, at an average speed of 6 kmph, reaches his school ten minutes before the school starts. When his average speed is 4 kmph, he reaches his school five minutes late. If he starts to school every day at 8.00 A.M, then find (i) the distance between his house and the school (ii) the minimum average speed to reach the school on time and time taken to reach the school (iii) the time the school gate closes (iv) the pair of straight lines of his path of walk.

Find the equation of the straight line passing through intersection of the straight lines 5x - 6y = 1 and 3x + 2y + 5 = 0 and perpendicular to the straight line 3x - 5y + 11=0.

Find the equation of the line, if the perpendicular drawn from the origin makes an angle 30° with x-axis and its length is 12

Find the equation of the line passing through the point (5, 2) and perpendicular to the line joining the points (2, 3) and (3, -1).

Show that the equation 9x² -24xy +16y² +12x + 16y -12 = 0 represents a pair parallel lines. find the distance between them

A straight line is passing through the point A(1,2) with slope \(\frac{5}{12}\). Find points on the line which are 13 units away from A.

Part - D

Generic 5 - Answer All Question

Rewrite √3x+y+4=0 in to normal form.

Find the equations of the straight lines in the family of the lines y = mx + 2, for which m and the x coordinate of the point of intersection of the lines with 2x + 3y = 10 are integers.

The sum of the distance of a moving point from the points (4,0) and (-4, 0) is always 10 units. Find the equation to the locus of the moving point.

Find the length of the perpendicular and the coordinates of the foot of the perpendicular form (-10, -2) to the line x + y - 2 = 0

Find the equations of straight lines which are perpendicular to the line 3x + 4y - 6 = 0 and are at a distance of 4 units from (2, 1).

Show that the points (1, 3), (2, 1) and \((\frac{1}{2},4)\) are collinear, by using
(i) concept of slope
(ii) a straight line
(iii) any other method.
Find the equation of the line passing through the point (1,5) and also co-ordinate axes in the ratio 3: 10.

Find the equation of the lines passing through the point of intersection lines 4x - y + 3 = 0 and 5x + 2y + 7 = 0
(i) through the point (-1, 2)
(ii) Parallel to x - y + 5 = 0
(iii) Perpendicular to x - 2y + 1 = 0.

Find the distance of the line 4x - y = 0 from the point p( 4,1) measured along the line making an angle of 135° with the positive x-axis.

If Q is a point on the locus of x²+y²+4x-3y+7=0, then find the equation of locus of P which divides segment OQ externally in the ratio 3: 4, where O is origin.

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11th Maths Monthly Test - 1(Two Dimensional Analytical Geometry)

St. Britto Hr. Sec. School - Madurai

11th Maths Monthly Test - 1(Two Dimensional Analytical Geometry)-Aug 2020

Part - A

Multiple Choice Question - Answer All Question

Slope of X-axis or a line parallel to X-axis is

The equation of the straight line upon which the length of perpendicular from the origin is p and this normal makes an angle \(\theta\) with the positive direction of x-axis is

The gradient of one of the lines of ax2+2hxy+by2=0 is twice that of the other, then

If the equation of the base opposite to the vertex (2,3) of an equilateral triangle is x +y = 2, then the length of a side is

Find the point of intersection of the lines 2x2+ xy -y2- 5x + 3y + 2 = 0:

The distance between the line 12x - 5y + 9 = 0 and the point (2, 1) is

The equation of a line which is equidistant from the lines x=-2 and x=6 is

The point (2,1) and (-3,5) are on

The distance between the parallel lines 3x-4y+9=0 and 6x-8y-15=0 is

If the points (a, 0) (0, b) and (x,y) are collinear, then

Part - B

Generic 2 - Answer All Question

Find the acute angle between the pair of lines given by 2x2-5xy-7y2 = 0.

Show that x2 - y2 + x - 3y - 2 = 0 represents a pair of straight lines. Find also angle between the lines.

Find the values of k for which the line (k-3)x-(4-k2)y+(k2-7k+6)=0 passes through the origin.

If \(\theta\) is the parameter, find the equation of the locus of a moving point, whose co-ordinates are x=a cos3 \(\theta\) ; y = without3 \(\theta\) .

Find the combined equation of the straight lines through the origin one of which is parallel to and the other is perpendicular to the straight line 3x + y + 5 = 0.

The sum of the squares of the distances of a moving point from two fixed points (a, 0) and (-0, 0) is equal to 2c2. Find the equation to its locus.

Find the combined equation of straight lines whose separate equations are x-2y-3=0 and x+y+5=0.

A straight line is drawn through the point p(2, 3) and is inclined at an angle of 30° with x-axis. Find the co-ordinates of two points on it at a distance of 4 from P on either side of P.

Find the equation of the line through the intersection of lines 3x+4y=7 and x-y+2=0 and whose slope is 5

Find the angle between the pair of straight lines given by (a2 - 3b2)x2 + 8ab xy+(b2 -3a2)y2 =0.

Part - C

Generic 3 - Answer All Question

Find the path traced out by the point \((ct,\frac{c}{t})\) , here t≠0 is the parameter and c is a constant.

Find the equation of the straight line which passes through the point (1, -2) and cuts off equal intercepts from axes.

Find the equation of the perpendicular bisector of the line segment joining the points A(2, 3) and B(6, -5).

Find the equation of a line with slope 2 and the length of the perpendicular from the origin is equal to \(\sqrt{5}\) .

Find the equation of the straight line passing through intersection of the straight lines 5x - 6y = 1 and 3x + 2y + 5 = 0 and perpendicular to the straight line 3x - 5y + 11=0.

Find the equation of the line, if the perpendicular drawn from the origin makes an angle 30° with x-axis and its length is 12

Find the equation of the line passing through the point (5, 2) and perpendicular to the line joining the points (2, 3) and (3, -1).

Show that the equation 9x2 -24xy +16y2 +12x + 16y -12 = 0 represents a pair parallel lines. find the distance between them

A straight line is passing through the point A(1,2) with slope \(\frac{5}{12}\). Find points on the line which are 13 units away from A.

Part - D

Generic 5 - Answer All Question

Rewrite √3x+y+4=0 in to normal form.

Find the equations of the straight lines in the family of the lines y = mx + 2, for which m and the x coordinate of the point of intersection of the lines with 2x + 3y = 10 are integers.

The sum of the distance of a moving point from the points (4,0) and (-4, 0) is always 10 units. Find the equation to the locus of the moving point.

Find the length of the perpendicular and the coordinates of the foot of the perpendicular form (-10, -2) to the line x + y - 2 = 0

Find the equations of straight lines which are perpendicular to the line 3x + 4y - 6 = 0 and are at a distance of 4 units from (2, 1).

Show that the points (1, 3), (2, 1) and \((\frac{1}{2},4)\) are collinear, by using (i) concept of slope (ii) a straight line (iii) any other method.

Find the equation of the line passing through the point (1,5) and also co-ordinate axes in the ratio 3: 10.

Find the equation of the lines passing through the point of intersection lines 4x - y + 3 = 0 and 5x + 2y + 7 = 0 (i) through the point (-1, 2) (ii) Parallel to x - y + 5 = 0 (iii) Perpendicular to x - 2y + 1 = 0.

Find the distance of the line 4x - y = 0 from the point p( 4,1) measured along the line making an angle of 135° with the positive x-axis.

If Q is a point on the locus of x2+y2+4x-3y+7=0, then find the equation of locus of P which divides segment OQ externally in the ratio 3: 4, where O is origin.

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The gradient of one of the lines of ax²+2hxy+by²=0 is twice that of the other, then

Find the point of intersection of the lines 2x²+ xy -y²- 5x + 3y + 2 = 0:

Find the acute angle between the pair of lines given by 2x²-5xy-7y² = 0.

Show that x² - y² + x - 3y - 2 = 0 represents a pair of straight lines. Find also angle between the lines.

Find the values of k for which the line (k-3)x-(4-k²)y+(k²-7k+6)=0 passes through the origin.

If \(\theta\) is the parameter, find the equation of the locus of a moving point, whose co-ordinates are x=a cos³\(\theta\) ; y = without³\(\theta\) .

The sum of the squares of the distances of a moving point from two fixed points (a, 0) and (-0, 0) is equal to 2c². Find the equation to its locus.

Find the angle between the pair of straight lines given by
(a² - 3b²)x² + 8ab xy+(b² -3a²)y² =0.

Show that the equation 9x² -24xy +16y² +12x + 16y -12 = 0 represents a pair parallel lines. find the distance between them

Show that the points (1, 3), (2, 1) and \((\frac{1}{2},4)\) are collinear, by using
(i) concept of slope
(ii) a straight line
(iii) any other method.

Find the equation of the lines passing through the point of intersection lines 4x - y + 3 = 0 and 5x + 2y + 7 = 0
(i) through the point (-1, 2)
(ii) Parallel to x - y + 5 = 0
(iii) Perpendicular to x - 2y + 1 = 0.

If Q is a point on the locus of x²+y²+4x-3y+7=0, then find the equation of locus of P which divides segment OQ externally in the ratio 3: 4, where O is origin.