Alpha Question Bank for Engineering: Mathematics>Chapter 18 - Ellipse>Exercise-1>Q 39

MEDIUM

JEE Main/Advance

IMPORTANT

Earn 100

The distance of the point of contact from the origin of the line $y = x - \sqrt{7}$ with the ellipse $3 x^{2} + 4 y^{2} = 12$

66.67% studentsanswered this correctly

Important Questions on Ellipse

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 18 - Ellipse>Exercise-1>Q 40

If

\frac{x}{a} + \frac{y}{b} = \sqrt{2}

touches the ellipse

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

at a point

P,

then eccentric angle of

P

is

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 18 - Ellipse>Exercise-1>Q 41

The point of intersection of the tangents at the point

P

on the ellipse

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

and its corresponding point

Q

on the auxiliary circle, lies on the line:

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 18 - Ellipse>Exercise-1>Q 42

The equation to the locus of the middle point of the portion of the tangent to the ellipse

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

included between the co-ordinate axes is the curve

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 18 - Ellipse>Exercise-1>Q 43

The equation of the chord of the ellipse

2 x^{2} + 5 y^{2} = 20

which is bisected at the point

(2, 1)

is

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 18 - Ellipse>Exercise-1>Q 44

Point, from which tangents to the ellipse

5 x^{2} + 4 y^{2} = 20

are not perpendicular, is:

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 18 - Ellipse>Exercise-1>Q 45

If the line

x cosα + y sinα = p

be normal to the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1,$ then

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 18 - Ellipse>Exercise-1>Q 46

If the focal chord of the ellipse

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

is normal at

(a \cos θ, bsin θ)

then eccentricity of the ellipse is (it is given that

\sin θ \neq 0

).

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Mathematics>Chapter 18 - Ellipse>Exercise-1>Q 47

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