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.

Comment

Add Comment

InstaQB

Institutions

12th Standard English Medium

12th Standard Tamil Medium

11th Standard English Medium

11th Standard Tamil Medium

10th Standard English Medium

9th Standard English Medium

8th Standard English Medium

7th Standard English Medium

Class XII

Class XI

12Th Standard

11Th Standard

10Th Standard

9Th Standard

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.

Comment

Other Study material

11th Maths Weekly Test - 3 ( Vector Algebra )

11th Maths Weekly Test -4 ( Vector Algebra )

11th Maths Monthly Test- 1 (Vector Algebra )

11th Maths Monthly Test -2( Vector Algebra )

11th Maths Monthly Test - 3 ( Vector Algebra )

11th Maths Monthly Test - 4 ( Vector Algebra )

11th Maths Weekly Test -1( Differential Calculus

11th Maths Weekly Test-2 ( Differential Calculus -

11th Maths Weekly Test - 3 ( Differential Calculus

11th Maths Weekly Test - 4 ( Differential Calculus

11th Maths Monthly Test -1( Differential Calculus

11th Maths Monthly Test -2( Differential Calculus

11th Maths Monthly Test - 3( Differential Calculu

11th Maths Monthly Test - 4 ( Differential Calcul

11th Maths Weekly Test - 1 ( Differential Calculus

Tamilnadu Stateboardszs - Class

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.