﻿ The locus of the mid-point of the chord of the circle x2 + y2 = 16, which are tangent to the hyperbola 9x2 – 16y2 = 144 is : Kaysons Education

# The Locus Of The Mid-point Of The Chord Of The Circle x2 + y2 = 16, Which Are Tangent To The Hyperbola 9x2 – 16y2 = 144 Is

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## Question

### Solution

Correct option is

(x2 + y2)= 16x2 – 9y2

9x2 – 16y= 144  ⇒ Equation of tangent to hyperbola is

…… (1)

…… (2)

Let (x1y1) be mid-point of the chord of circle x2 + y= 16 equation of this is

x x1 + y y1  (x12 + y12) = 0                        …… (3)

so

eliminate m to get locus of (x1y1) as

(x2 + y2)= 16x2 – 9y2

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