Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 13

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JEE Main

IMPORTANT

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If $12 x = k$ is the directrix of parabola $y^{2} + 4 y + 3 x = 0,$ then which of the following are true?

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Important Questions on Conic Section

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JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 14

The mirror image of the parabola $y^{2} = 4 x$ in the tangent at $(1, 2)$ to it, is

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 15

Equation

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

represents -

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JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 16

The following line(s) is (are) tangent to the curve $y = x^{2} - x$

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 17

The normals to the parabola

y^{2} = 4 a x

from the point

(5 a, 2 a)

are -

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Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 18

The equation of tangent to the parabola

y^{2} = 9 x

which goes through the point

(4, 10),

is

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JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 19

If

f (x + y) = f (x) \cdot f (y)

for all

x, y

and

f (1) = 2

and

a_{r} = f (r), r \in N

, then the coordinates of a point on the parabola

y^{2} = 8 x

whose focal distance is

4

may be

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JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 20

If pair of tangents are drawn to the ellipse

\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1

from a point

P

so that the tangents are at right angles to each other, then the possible coordinates of the point

P

is/are

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JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 21

If latus rectum of ellipse

x^{2} \tan^{2} ϕ + y^{2} \sec^{2} ϕ = 1

is

1 / 2

, then

(0 < ϕ < π)

is equal to