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Hyperbola question

2022 · Shift 2 · Q25

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PYQ Library
JEE Advanced
Mathematics
Hyperbola
2022 · Shift 2 · Q25

Hyperbola question

2022 · Shift 2 · Q25

JEE AdvancedMathematicsHyperbolaNumerical+3 / −1

Consider the hyperbola

\frac{x^{2}}{100}-\frac{y^{2}}{64}=1

with foci at

S

and

S_{1}

, where

S

lies on the positive

x

-axis. Let

P

be a point on the hyperbola, in the first quadrant. Let

\angle S P S_{1}=\alpha

, with

\alpha\lt \frac{\pi}{2}

. The straight line passing through the point

S

and having the same slope as that of the tangent at

P

to the hyperbola, intersects the straight line

S_{1} P

at

P_{1}

. Let

\delta

be the distance of

P

from the straight line

S P_{1}

, and

\beta=S_{1} P

. Then the greatest integer less than or equal to

\frac{\beta \delta}{9} \sin \frac{\alpha}{2}

is

\underline{\hspace{2cm}}

.

Numerical answer

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