If the eccentricity of the ellipse $\frac{x^2}{a^2+2}+\frac{y^2}{a^2+5}=1$ be $\frac{1}{\sqrt{3}}$, then length of latus rectum of ellipse is

JEE MATHEMATICS MCQ: ELLIPSE

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Application +4 | -1

If the eccentricity of the ellipse

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

\frac{1}{\sqrt{3}}

, then length of latus rectum of ellipse is

View answer and explanation

Correct option: A

Option A (4) is correct because the length of the latus rectum of the ellipse is calculated by first finding the values of a and b using the given eccentricity and then applying the formula for the latus rectum.

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Let

\frac{x^2}{144}+\frac{y^2}{81}=1

be the equation of an ellipse. If

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be the minimum value of the segment of tangent to the ellipse intercepted by the coordinate axes and

\mathrm{M}

be the maximum distance of the centre of the ellipse from the normal, then the value of

\mathrm{mM}

is equal to Let

P

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\frac{{{x^2}}}{{25}} + \frac{{{y^2}}}{{16}} = 1

with foci at

S

and

S'.

A

be the area of triangle

PSS',

then the maximum value of

A

is If the co-ordinates of two points

A

and

B

are

(\sqrt{7}, 0)

and

(-\sqrt{7}, 0)

respectively and

P

is any point on the conic,

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

, then

\mathrm{PA}+\mathrm{PB}

is equal to :
The slope of a common tangent to the ellipse

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

and a concentric circle of radius

r

, is A tangent to the ellipse

\frac{x^2}{25}+\frac{y^2}{16}=1

at any point

P

meet the line

x=0

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Q

. Let

R

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Q

in the line

y=x

, then circle whose extremities of a diameter are

Q

and

R

passes through a fixed point. The fixed point is Any ordinate

N P

of an ellipse meets the auxiliary circle at

Q

. Then, the locus of the intersection of the normal at

P

and

O

is the circle