﻿ If SK perpendicular from focus S on th tangent at any point P of the hyperbola  , then K lies on : Kaysons Education

# If SK perpendicular From Focus S on Th Tangent At Any Point P of The Hyperbola  , Then K lies On

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## Question

### Solution

Correct option is

Auxiliary circle

Any tangent to hyperbola

….. (1)

Any line ⊥ to (1) is x + my = c                  ….. (2)

(2) Passes through S(ae, 0) ∴ C = ae.

Now (2) ⇒ x + my = ae

The locus of k, the feet of perpendicular is obtained …. (3)

By eliminating m between (1) & (3). Square & add (1) and (3).

⇒ x2 + y2 = a2 which is auxiliary circle.

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