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#### Two Dimensional Analytical Geometry - II Model Questions

12th Standard EM

Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 50
5 x 1 = 5
1. The equation of the circle passing through(1,5) and (4,1) and touching y -axis is x2+y2−5x−6y+9+(4x+3y−19)=0 whereλ is equal to

(a)

$0,-\frac { 40 }{ 9 }$

(b)

0

(c)

$\frac { 40 }{ 9 }$

(d)

$\frac { -40 }{ 9 }$

2. The centre of the circle inscribed in a square formed by the lines x2−8x−12=0 and y2−14y+45 = 0 is

(a)

(4,7)

(b)

(7,4)

(c)

(9,4)

(d)

(4,9)

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. Equation of tangent at (-4, -4) on x2 = -4y is

(a)

2x - y + 4 = 0

(b)

2x + y - 4 = 0

(c)

2x - y - 12 = 0

(d)

2x + y + 4 = 0

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

(a)

circle

(b)

parabola

(c)

ellipse

(d)

hyperbola

6. 5 x 2 = 10
7. The line 3x+4y−12 = 0 meets the coordinate axes at A and B . Find the equation of the circle drawn on AB as diameter.

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

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

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

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

12. 5 x 3 = 15
13. Find the centre and radius of the circle3x2+(a+1)y2+6x−9y+a+4=0.

14. Find the equation of the tangent and normal to the circle x2+y2−6x+6y−8=0 at (2,2) .

15. Find the equation of the hyperbola whose conjugate axis is 5 and the distance between the foci is 13.

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. On lighting a rocket cracker it gets projected in a parabolic path and reaches a maximum height of 4m when it is 6m away from the point of projection. Finally it reaches the ground 12m away from the starting point. Find the angle of projection.

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.