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#### Two Dimensional Analytical Geometry II Two Marks Questions

12th Standard EM

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
15 x 2 = 30
1. Find the general equation of a circle with centre(-3,-4) and radius 3 units.

2. Find the general equation of the circle whose diameter is the line segment joining the points (−4,−2)and (1,1).

3. Examine the position of the point (2,3) with respect to the circle x2+y2−6x−8y+12=0.

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

5. Obtain the equation of the circle for which (3,4) and (2,-7) are the ends of a diameter.

6. 2x2−y2=7

7. 3x2+2y2=14

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

9. Find centre and radius of the following circles.
x2+y2−x+2y−3= 0

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

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

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

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

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 = $\frac { 4 }{ 3 }$