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#### Two Dimensional Analytical Geometry II One Mark Questions with Answer

12th Standard EM

Reg.No. :
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Maths

Time : 00:45:00 Hrs
Total Marks : 25
25 x 1 = 25
1. The equation of the directrix of the parabola y2+ 4y + 4x + 2 = 0 is

(a)

x = -1

(b)

x = 1

(c)

x = $\frac{-3}{2}$

(d)

x = $\frac{3}{2}$

2. 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

3. 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)

4. The eccentricity of the ellipse 9x2+ 5y2 - 30y= 0 is

(a)

$\frac13$

(b)

$\frac23$

(c)

$\frac34$

(d)

none of these

5. The length of the latus rectum of the ellipse $\frac { { x }^{ 2 } }{ 36 } +\frac { { y }^{ 2 } }{ 49 }$ = 1 is

(a)

$\frac { 98 }{ 6 }$

(b)

$\frac { 72 }{ 7 }$

(c)

$\frac { 72 }{ 14 }$

(d)

$\frac { 98 }{ 12 }$

6. In an ellipse, the distance between its foci is 6 and its minor axis is 8, then e is

(a)

$\frac { 4 }{ 5 }$

(b)

$\frac { 1 }{ \sqrt { 52 } }$

(c)

$\frac { 3 }{ 5 }$

(d)

$\frac { 1 }{ 2 }$

7. The equation 7x2- 6$\sqrt { 3 }$ xy + 13y2 - 4$\sqrt { 3 }$ x - 4y - 12 = 0 represents

(a)

parabola

(b)

ellipse

(c)

hyperbola

(d)

rectangular hyperbola

8. The distance between the foci of a hyperbola is 16 and e = $\sqrt { 2 }$ Its equation is

(a)

x2 - y2 = 32

(b)

y2 - x2 = 32

(c)

x2 - y2 = 16

(d)

y2 - x2 = 16

9. When the eccentricity of a ellipse becomes zero, then it becomes a

(a)

straight line

(b)

circle

(c)

point

(d)

parabola

10. The auxiliary circle of the ellipse $\frac { { x }^{ 2 } }{ 25 } +\frac { { y }^{ 2 } }{ 16 }$ = 1 is

(a)

x2 + y2 = 25

(b)

x2 + y2 = 16

(c)

x2 + y2 = 41

(d)

x2 + y2 = 5

11. The length of the diameter of a circle with centre (1, 2) and passing through (5, 5) is

(a)

5

(b)

$\sqrt{45}$

(c)

10

(d)

$\sqrt{50}$

12. If (1, -3) is the centre of the circle x+ y+ ax + by + 9 = 0 its radius is

(a)

$\sqrt{10}$

(b)

1

(c)

5

(d)

$\sqrt{19}$

13. The equation of tangent at (1, 2) to the circle x+ y2 = 5 is

(a)

x+y=3

(b)

x + 2y = 3

(c)

x- y= 5

(d)

x - 2y = 5

14. If y = 2x + c is a tangent to the circle x2 + y2 = 5, then c is

(a)

土5

(b)

$\sqrt5$

(c)

土5$\sqrt2$

(d)

±2$\sqrt5$

15. The line y = mx +1 is a tangent to the parabola y2 = 4x if m = ______________

(a)

1

(b)

2

(c)

3

(d)

4

16. The angle between the tangents drawn from (1, 4) to the parabola y2 = 4x is __________

(a)

$\frac { \pi }{ 2 }$

(b)

$\frac { \pi }{ 3 }$

(c)

$\frac { \pi }{ 5 }$

(d)

$\frac { \pi }{ 5 }$

17. In an ellipse 5x2 + 7y2 = 11, the point (4, -3) lies _________ the ellipse

(a)

on

(b)

outside

(c)

inside

(d)

none

18. The number of normals to the hyperbola $\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } }$ = 1 from an external point is

(a)

2

(b)

4

(c)

6

(d)

5

19. The point of contact of y2 = 4ax and the tangent y = mx + c is

(a)

$\left( \frac { 2a }{ { m }^{ 2 } } ,\frac { a }{ m } \right)$

(b)

$\left( \frac { a }{ { m }^{ 2 } } ,\frac { 2a }{ m } \right)$

(c)

$\left( \frac { a }{ m} ,\frac { 2a }{ { m }^{ 2 } } \right)$

(d)

$\left( \frac {-a }{ { m }^{ 2 }} ,\frac {- 2a }{ m } \right)$

20. If B, B1 are the ends of minor axis, F1 ,F2 are foci of the ellipse $\frac { { x }^{ 2 } }{ 8 } +\frac { { y }^{ 2 } }{ 4 }$ = 1 then area of F1BF2B1 is

(a)

16

(b)

8

(c)

16$\sqrt2$

(d)

32$\sqrt2$

21. The length of major and minor axes of 4x2 + 3y2 = 12 are ____________

(a)

4, 2$\sqrt3$

(b)

2, $\sqrt3$

(c)

2$\sqrt3$, 4

(d)

$\sqrt3$, 2

22. The tangent at any point P on the ellipse $\frac { { x }^{ 2 } }{ 6 } +\frac { { y }^{ 2 } }{ 3 }$ = 1 whose centre C meets the major axis at T and PN is the perpendicular to the major axis; The CN CT = ______________

(a)

$\sqrt6$

(b)

3

(c)

$\sqrt3$

(d)

6

23. The locus of the point of Inter eetton of perpendicular tangents to the hyperbela $\frac { { x }^{ 2 } }{ 16 } +\frac { { y }^{ 2 } }{ 9 }$ = 1 is __________

(a)

x2+y2= 25

(b)

x2 +y2 = 4.

(c)

x2 +y2 = 3

(d)

x2+y2=7

24. Th point of curve y = 2x2 - 6x - 4 at which the targent is parallel to x - axis is

(a)

$\left( \frac { 5 }{ 2 } ,\frac { -7 }{ 12 } \right)$

(b)

$\left( \frac { -5 }{ 2 } ,\frac { -7 }{ 2 } \right)$

(c)

$\left( \frac { -5 }{ 2 } ,\frac { 17 }{ 12 } \right)$

(d)

$\left( \frac { 3 }{ 2 } ,\frac { -7 }{ 2 } \right)$

25. The locus of the point of intersection of perpendicular tangents of the parabola y2 = 4ax is

(a)

latus rectum

(b)

directrix

(c)

tangent at the vertex

(d)

axis of the parabola