11th Maths Weekly Test - 2 (Two Dimensional Analytical Geometry)

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test - 2 (Two Dimensional Analytical Geometry)-Aug 2020

Time : 1.30 Hours

Part - A

Generic 2 - Answer All Question

Find the value of a and p if the equation x-cos a + y sin a =p is the normal form of the line \(\sqrt{3x}+y+2=0\)

Define locus? write any one example.

Two sides of a square lie on the lines x + y =1 and x + y + 2 = 0.What is its area?

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 lines 3x² + 10xy + 8y² + 14x + 22y + 15 = 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.

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 locus of P, if for all values of \(\alpha\) the co-ordinates of a moving point P is
(i) (9 cos,\(\alpha\) 9 sin \(\alpha\))
(ii) (9 cos \(\alpha\), 6 sin \(\alpha\))

Prove that the straight lines joining the origin to the points of intersection of 3x²+5xy-3y²+2x + 3y = 0 and 3x - 2y - 1 = 0 are at right angles.

Determine the equation of line through the point (-4, -3) and perpendicular to y-axis.

Part - B

Generic 5 - Answer All Question

A line is drawn perpendicular to 5x = y + 7. Find the equation of the line if the area of the triangle formed by this line with co-ordinate axes is 10 sq. units.

A \(\triangle\) OPQ is formed by the pair of straight lines x² - 4xy + y² = 0 and the line PQ. The equation of PQ is x + y - 2 = 0 . Find the equation of the median of the triangle \(\triangle\)OPQ drawn from the origin O.

Show that the straight lines joining the origin to the points of intersection of 3x - 2y + 2 = 0 and 3x² + 5xy - 2y² + 4x + 5y = 0 are at right angles.

Find the equations of a parallel line and a perpendicular line passing through the point (1, 2) to the line 3x + 4y = 7.

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11th Maths Weekly Test - 2 (Two Dimensional Analytical Geometry)

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test - 2 (Two Dimensional Analytical Geometry)-Aug 2020

Part - A

Generic 2 - Answer All Question

Find the value of a and p if the equation x-cos a + y sin a =p is the normal form of the line \(\sqrt{3x}+y+2=0\)

Define locus? write any one example.

Two sides of a square lie on the lines x + y =1 and x + y + 2 = 0.What is its area?

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 lines 3x2 + 10xy + 8y2 + 14x + 22y + 15 = 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.

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 locus of P, if for all values of \(\alpha\) the co-ordinates of a moving point P is (i) (9 cos,\(\alpha\) 9 sin \(\alpha\)) (ii) (9 cos \(\alpha\), 6 sin \(\alpha\))

Prove that the straight lines joining the origin to the points of intersection of 3x2+5xy-3y2+2x + 3y = 0 and 3x - 2y - 1 = 0 are at right angles.

Determine the equation of line through the point (-4, -3) and perpendicular to y-axis.

Part - B

Generic 5 - Answer All Question

A line is drawn perpendicular to 5x = y + 7. Find the equation of the line if the area of the triangle formed by this line with co-ordinate axes is 10 sq. units.

A \(\triangle\) OPQ is formed by the pair of straight lines x2 - 4xy + y2 = 0 and the line PQ. The equation of PQ is x + y - 2 = 0 . Find the equation of the median of the triangle \(\triangle\)OPQ drawn from the origin O.

Show that the straight lines joining the origin to the points of intersection of 3x - 2y + 2 = 0 and 3x2 + 5xy - 2y2 + 4x + 5y = 0 are at right angles.

Find the equations of a parallel line and a perpendicular line passing through the point (1, 2) to the line 3x + 4y = 7.

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Find the angle between the lines 3x² + 10xy + 8y² + 14x + 22y + 15 = 0.

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 locus of P, if for all values of \(\alpha\) the co-ordinates of a moving point P is
(i) (9 cos,\(\alpha\) 9 sin \(\alpha\))
(ii) (9 cos \(\alpha\), 6 sin \(\alpha\))

Prove that the straight lines joining the origin to the points of intersection of 3x²+5xy-3y²+2x + 3y = 0 and 3x - 2y - 1 = 0 are at right angles.

A \(\triangle\) OPQ is formed by the pair of straight lines x² - 4xy + y² = 0 and the line PQ. The equation of PQ is x + y - 2 = 0 . Find the equation of the median of the triangle \(\triangle\)OPQ drawn from the origin O.

Show that the straight lines joining the origin to the points of intersection of 3x - 2y + 2 = 0 and 3x² + 5xy - 2y² + 4x + 5y = 0 are at right angles.