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Hyperbola question

2024 · 4 Apr · Shift 2 · Q31

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JEE Main
Mathematics
Hyperbola
2024 · 4 Apr · Shift 2 · Q31

Hyperbola question

2024 · 4 Apr · Shift 2 · Q31

JEE MainMathematicsHyperbolaMCQ+4 / −1

Consider a hyperbola

\mathrm{H}

having centre at the origin and foci on the

\mathrm{x}

-axis. Let

\mathrm{C}_1

be the circle touching the hyperbola

\mathrm{H}

and having the centre at the origin. Let

\mathrm{C}_2

be the circle touching the hyperbola

\mathrm{H}

at its vertex and having the centre at one of its foci. If areas (in sq units) of

C_1

and

C_2

are

36 \pi

and

4 \pi

, respectively, then the length (in units) of latus rectum of

\mathrm{H}

is

A
$\frac{28}{3}$
B
$\frac{11}{3}$
C
$\frac{14}{3}$
D
$\frac{10}{3}$

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