Mathematics Crash Course JEE Main>Chapter 10 - Ellipse>Level 1>Q 10

MEDIUM

JEE Main

IMPORTANT

Earn 100

The centre of the ellipse $\frac{(x + y - 3)^{2}}{9} + \frac{(x - y + 1)^{2}}{16} = 1$ is

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Important Questions on Ellipse

EASY

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 10 - Ellipse>Level 1>Q 11

If

P \equiv (x, y), F_{1} \equiv (3, 0), F_{2} \equiv (- 3, 0)

and

16 x^{2} + 25 y^{2} = 400

, then

P F_{1} + P F_{2}

equals

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 10 - Ellipse>Level 1>Q 13

For what value of

λ

does the line

y = x + λ

touches the ellipse

9 x^{2} + 16 y^{2} = 144

.

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 10 - Ellipse>Level 1>Q 14

The minimum area of the triangle formed by any tangent to the ellipse

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

with the coordinate axes is

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 10 - Ellipse>Level 1>Q 15

Let

L

be a common tangent line to the curves

4 x^{2} + 9 y^{2} = 36

and

{(2 x)}^{2} + {(2 y)}^{2} = 31

. Then the square of the slope of the line

L

is ______.

MEDIUM

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 10 - Ellipse>Level 1>Q 16

If

(\sqrt{3}) b x + a y = 2 a b

touches the ellipse

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1,

then the eccentric angle of the point of contact is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 10 - Ellipse>Level 1>Q 17

The equation of the normal to the ellipse

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

at the end of the latus rectum in the first quadrant is

MEDIUM

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 10 - Ellipse>Level 1>Q 18

The equation of the tangents to the ellipse

9 x^{2} + 16 y^{2} = 144

which passes through the point

(2, 3)

is

EASY

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 10 - Ellipse>Level 1>Q 19

If

F_{1}

and

F_{2}

are the foot of the perpendiculars from the foci

S_{1}

and

S_{2}

of an ellipse

\frac{x^{2}}{5} + \frac{y^{2}}{3} = 1

on the tangent at any point

P

on the ellipse, then

(S_{1} F_{1}) (S_{2} F_{2})

is equal to