" /> -->

#### Two Dimensional Analytical Geometry II - Two Marks Study Materials

12th Standard EM

Reg.No. :
•
•
•
•
•
•

Maths

Time : 01:00:00 Hrs
Total Marks : 30
15 x 2 = 30
1. Examine the position of the point (2,3) with respect to the circle x2+y2−6x−8y+12=0.

2. Find the equation of the circle with centre (2,-1) and passing through the point (3,6) in standard form.

3. 11x2−25y2−44x+50y−256 = 0

4. Find centre and radius of the following circles.
x2+y2+6x−4y+4=0

5. Find centre and radius of the following circles.
2x2+2y2−6x+4y+2=0

6. Find the equation of tangent to the circle x2 +y2 + 2x - 3y - 8 = 0 at (2, 3).

7. Find the length of the tangent from (2, -3) to the circle x2 + y2 - 8x - 9y + 12 = 0.

8. Find the equation of the parabola with vertex at the origin, passing through (2, -3) and symmetric about x-axis

9. If a parabolic reflector is 24 cm in diameter and 6 cm deep, find its locus.

10. If the line y = 3x + 1, touches the parabola y2 = 4ax, find the length of the latus rectum?

11. Find the locus of a point which divides so that the sum of its.distances from (-4, 0) and (4, 0) is 10 units.

12. For the ellipse x2 + 3y2 = a2, find the length of major and minor axis.

13. Find the eccentricity of the ellipse with foci on x-axis if its latus rectum be equal to one half of its major axis.

14. Find the eccentricity of the hyperbola. with foci on the x-axis if the length of its conjugate axis is ${ \left( \frac { 3 }{ 4 } \right) }^{ th }$ of the length of its tranverse axis.

15. Find the equation of the hyperbola whose vertices are (0, ±7) and e = $\frac { 4 }{ 3 }$