Let ${H}: {xy}-{y}-2 {x}-2=0$. If normal drawn to ${H}$ at ${P}(3,4)$ intersects the curve again at $Q(\alpha+1, \beta+1)$, then $\frac{\alpha}{\beta}$ is

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JEE • MATHEMATICS • HYPERBOLIC FUNCTIONS

Hyperbolic functions practice · Medium

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Analyzing +4 | -1

Let

{H}: {xy}-{y}-2 {x}-2=0

. If normal drawn to

{H}

{P}(3,4)

intersects the curve again at

Q(\alpha+1, \beta+1)

, then

\frac{\alpha}{\beta}

View answer and explanation

Correct option: A

Option A (2) is correct because after transforming the hyperbola to its standard form and finding the normal at P, the ratio α/β is calculated to be 2.

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Hyperbolic functions practice · Medium

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