Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-1>Q 31

HARD

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IMPORTANT

Earn 100

Find the equation of a circle touching the parabola $y^{2} = 8 x$ at $(2, 4)$ and passing through $(0, 4) .$

Important Questions on Parabola

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-1>Q 32

The equation of the parabola whose focus is

(- 3, 0)

and the directrix is

x + 5 = 0

is

MEDIUM

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-1>Q 33

If

(2, 0)

is the vertex and

Y

-axis is the directrix of a parabola, then its focus is

MEDIUM

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-1>Q 34

Length of the latus rectum of the parabola

25 [{(x - 2)}^{2} + {(y - 3)}^{2}] = {(3 x - 4 y + 7)}^{2}

is

MEDIUM

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-1>Q 35

A parabola is drawn with its focus at

(3, 4)

and vertex at the focus of the parabola

y^{2} - 12 x - 4 y + 4 = 0

. The equation of the parabola is

HARD

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-1>Q 36

Which one of the following equations parametrically represents equation to a parabolic profile?

MEDIUM

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-1>Q 37

The points on the parabola

y^{2} = 12 x

whose focal distance is

4

, are

EASY

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-1>Q 38

Find all the possible values of

α

such that point

P (α, α)

is outside the parabola

y = x^{2} + x + 1

.

MEDIUM

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IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 17 - Parabola>Exercise-1>Q 39

If on a given base, a triangle be described such that the sum of the tangents of the base angles is a constant, then the locus of the vertex is