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#### Two Dimensional Analytical Geometry Two Marks Question

11th Standard

Reg.No. :
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Maths

Time : 00:45:00 Hrs
Total Marks : 30
15 x 2 = 30
1. 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.

2. Determine x so that the line passing through (3, 4) and (x, 5) makes 135° with the positive direction of x-axis.

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

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

5. If 9x2 + 12xy + 4y2 + 6x + 4y - 3 = 0 represents two parallel lines, find the distance between them.

6. If the line y = mx is one of the bisectors of the lines x2 + 4xy - y2 = 0, then find m.

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

8. Find the equation of straight line joining the points of intersection of the lines 3x + 2y + 1 = 0 and x + y = 3 to the intersection of the lines y - x = 1 and 2x + y +2 = 0.

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

10. 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.

11. If the equation 12x2 - 10xy + 2y2 + 14x - 5y + k = 0 represents a pair of straight lines, find k, find separate equation and also angle between them.

12. If $\theta$  is the parameter, find the equation of the locus of a moving point, whose co-ordinates are x=a cos3 $\theta$ ; y = without$\theta$ .

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

14. A line passing through the points (a, 2a) and (-2, 3) is perpendicular to the line 4x+3y+ 5 = 0, find the value of a.

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