An incident ray reflects at A = ( − 2 , 3 ) on a 2 x 2 − b 2 y 2 = 1 and the reflected ray passes through focus S = ( 2 , 0 ) . Which statements are true?

Mathematics - Hyperbola Question with Solution | TestHub

MathematicsHyperbolaTangents & NormalsMedium2 minQB

MathematicsMediummultiple choice

An incident ray reflects at $A = (- 2, 3)$ on $\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1$ and the reflected ray passes through focus $S = (2, 0)$ . Which statements are true?

Options:(select one or more)

Answer:

A, B, C, D

Solution:

The other focus is $(- 2, 0)$ , so the incident ray is $x = - 2$ and the reflected ray through $A, S$ is $3 x + 4 y = 6$ . Since $a e = 2$ and $A$ lies on the hyperbola, $a = 1, e = 2$ , giving latus rectum $2 a (e^{2} - 1) = 6$ .

Stream:JEESubject:MathematicsTopic:HyperbolaSubtopic:Tangents & Normals

⏱ 2mℹ️ Source: QB

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