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 = \(\frac{3}{2}\)

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

If a parabolic reflector is 20 cm in diameter and 5 cm in diameter and 5 cm deep, then its focus is ____________

(a)

(0, 5)

(b)

(5, 0)

(c)

(10, 0)

(d)

(0, 10)

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

(a)

\(\frac13\)

(b)

\(\frac23\)

(c)

\(\frac34\)

(d)

none of these

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)

\(\frac { 98 }{ 12 } \)

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)

\(\frac { 1 }{ 2 } \)

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

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

When the eccentricity of a ellipse becomes zero, then it becomes a __________

(a)

straight line

(b)

circle

(c)

point

(d)

parabola

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

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)

\(\sqrt{50}\)

If (1, -3) is the centre of the circle x² + y² + ax + by + 9 = 0 its radius is _________

(a)

\(\sqrt{10}\)

(b)

1

(c)

5

(d)

\(\sqrt{19}\)

The equation of tangent at (1, 2) to the circle x² + y² = 5 is __________

(a)

x + y = 3

(b)

x + 2y = 3

(c)

x- y = 5

(d)

x - 2y = 5

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

(a)

土5

(b)

土\(\sqrt5\)

(c)

土5\(\sqrt2\)

(d)

±2\(\sqrt5\)

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

(a)

1

(b)

2

(c)

3

(d)

4

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)

\(\frac { \pi }{ 5 } \)

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

(a)

on

(b)

outside

(c)

inside

(d)

none

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

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)

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

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\(\sqrt2\)

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

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

The locus of the point of Intersection 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

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)

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

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