EASY

Earn 100

Explain degenerate case of parabola?

Important Questions on Conic Sections

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>Sections of a Cone

The directrix of the parabola

2 y^{2} + 25 x = 0

is _________

EASY

Mathematics>Coordinate Geometry>Conic Sections>Sections of a Cone

The vertex of the parabola

y = x^{2} - 2 x + 4

is shifted

p

units to the right and then

q

units up. If the resulting point is

(4, 5),

then the values of

p

and

q

respectively are

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>Sections of a Cone

The equation

y^{2} + 3 = 2 (2 x + y)

represents a parabola with the vertex at

HARD

Mathematics>Coordinate Geometry>Conic Sections>Sections of a Cone

For the parabola

y^{2} + 6 y - 2 x + 5 = 0,

match the items in List-

I

with the suitable item in List-

II

given below:

List- $I$		List- $II$
$(I)$	Vertex	$(A)$	$(- \frac{3}{2}, - 3)$
$(II)$	Focus	$(B)$	$(\frac{3}{2}, - 3)$
$(III)$	Equation of the directrix	$(C)$	$2 x + 5 = 0$
$(IV)$	Equation of the axis	$(D)$	$2 x + y + 3 = 0$
		$(E)$	$y + 3 = 0$
		$(F)$	$(- 2, - 3)$

The correct matching is

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>Sections of a Cone

The focus of the parabola

y^{2} - 4 y - x + 3 = 0

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>Sections of a Cone

The length of latus rectum of the parabola whose focus is at

(1, - 2)

and directrix is the line

x + y + 3 = 0

EASY

Mathematics>Coordinate Geometry>Conic Sections>Sections of a Cone

The vertex of the parabola

y = (x - 2) (x - 8) + 7

HARD

Mathematics>Coordinate Geometry>Conic Sections>Sections of a Cone

The equation of the lines joining the vertex of the parabola

y^{2} = 6 x

to the point on it which have abscissa

24

are

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>Sections of a Cone

The focus of the parabola

{(y + 1)}^{2} = - 8 (x + 2)

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>Sections of a Cone

The centres of those circles which touch the circle,

x^{2} + y^{2} - 8 x - 8 y - 4 = 0,

externally and also touch the

x

- axis, lie on

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>Sections of a Cone

The equation of the latus rectum of a parabola is

x + y = 8

and the equation of the tangent at the vertex is

x + y = 12 .

Then, the length of the latus rectum is

HARD

Mathematics>Coordinate Geometry>Conic Sections>Sections of a Cone

A cable of a suspension bridge is in the form of a parabola whose span is $40$ metres. The road way is $5$ metres below the lowest point of the cable. An extra support is provided across the cable $30$ metres above the ground level. Find the length of the support if the height of the pillars are $55$ metres.

EASY

Mathematics>Coordinate Geometry>Conic Sections>Sections of a Cone

The two ends of a latus rectum of a parabola are

(5, 8)

and

(- 7, 8)

. Then its focus is

EASY

Mathematics>Coordinate Geometry>Conic Sections>Sections of a Cone

If the parabola

x^{2} = 4 a y

passes through the point

(2, 1)

, then the length of the latus rectum is

HARD

Mathematics>Coordinate Geometry>Conic Sections>Sections of a Cone

Equation of the directrix of the parabola whose focus is

(0, 0)

and the tangent at the vertex is

x - y + 1 = 0

EASY

Mathematics>Coordinate Geometry>Conic Sections>Sections of a Cone

The length of the Latus rectum of the parabola

x = a y^{2} + b y + c

EASY

Mathematics>Coordinate Geometry>Conic Sections>Sections of a Cone

The curved described parametrically by

x = t^{2} + t + 1

and

y = t^{2} - t + 1

represents:

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>Sections of a Cone

The equation of the directrix of the parabola

x^{2} - 4 x - 3 y + 10 = 0

HARD

Mathematics>Coordinate Geometry>Conic Sections>Sections of a Cone

Suppose the parabola

{(y - k)}^{2} = 4 (x - h),

with vertex

A

, passes through

O = (0, 0)

and

L = (0, 2) .

Let

D

be an end point of the latus rectum. Let the

y

-axis intersect the axis of the parabola at

P

. Then

∠ P D A

is equal to

MEDIUM

Mathematics>Coordinate Geometry>Conic Sections>Sections of a Cone

a x^{2} + 2 h x y + b y^{2} - 82 x + 98 y + 144 = 0

is the equation of a parabola with focus

(2, - 3)

and directrix

3 x - 2 y + 5 = 0,

then

a x^{2} + 2 h x y + b y^{2} = 0

represents

Explain degenerate case of parabola?

Important Questions on Conic Sections

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