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#### Two Dimensional Analytical Geometry-II Model Question Paper 1

12th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
5 x 1 = 5
1. The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half the distance between the foci is

(a)

$\frac { 4 }{ 3 }$

(b)

$\frac { 4 }{ \sqrt { 3 } }$

(c)

$\frac { 2 }{ \sqrt { 3 } }$

(d)

$\frac { 3 }{ 2 }$

2. The equation of the normal to the circle x2+y2−2x−2y+1=0 which is parallel to the line
2x+4y=3 is

(a)

x+2y=3

(b)

x+2y+3= 0

(c)

2x+4y+3=0

(d)

x−2y+3= 0

3. If x+y=k is a normal to the parabola y2 =12x, then the value of k is

(a)

3

(b)

-1

(c)

1

(d)

9

4. y2 - 2x - 2y + 5 = 0 is a

(a)

circle

(b)

parabola

(c)

ellipse

(d)

hyperbola

5. If a parabolic reflector is 20 em in diameter and 5 em deep, then its focus is

(a)

(0,5)

(b)

(5,0)

(c)

(10,0)

(d)

(0, 10)

6. 5 x 2 = 10
7. Find the equation of the circle with centre (2,-1) and passing through the point (3,6) in standard form.

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

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

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

11. 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.

12. 5 x 3 = 15
13. Find the equations of the tangent and normal to the circle x2+y2=25 at P(-3,4).

14. Find the equation of circles that touch both the axes and pass through (-4,-2) in general form.

15. Find the area of th triangle found by the Unel Joining the vertex of the parabola x2 = -36y to the ends of the latus rectum.

16. For the hyperbola 3x2 - 6y2 = -18, find the length of transverse and conjugate axes and eccentricity.

17. Find the value of c if y = x + c is a tangent to the hyperbola 9x2 - 16y2 = 144.

18. 4 x 5 = 20
19. Find the vertex, focus, directrix, and length of the latus rectum of the parabola x2−4x−5y−1=0.

20. Find the equation of the ellipse whose eccentricity is $\frac { 1 }{ 2 }$, one of the foci is(2,3) and a directrix is x = 7 . Also find the length of the major and minor axes of the ellipse.

21. The foci of a hyperbola coincides with the foci of the ellipse $\frac { { x }^{ 2 } }{ 25 } +\frac { y^{ 2 } }{ 9 } =1$. Find the equation of the hyperbola if its eccentricity is 2.

22. A kho-kho player In a practice Ion while running realises that the sum of tne distances from the two kho-kho poles from him is always 8m. Find the equation of the path traced by him of the distance between the poles is 6m.