Find the locus of the mid points of the chords of the circle x 2 + y 2 = 16, which are tangent to the hyperbola 9 x 2 − 16 y 2 = 144.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(x 2 + y 2 ) 2 = 16 x 2 - 9 y 2
Sol. Let (h,k) be the mid pt of the chord of the circle x 2 + y 2 = 16
∴ the equation of the chord will be
hx + ky = h 2 + k 2
or y = 
x + 
i.e. of the form y = mx + C.
It will touch the hyperbola if C 2 = a 2 m 2 – b 2
∴ 
= 16 
– 9
⇒ (h 2 + k 2 ) 2 = 16 h 2 – 9k 2
∴ required locus is (x 2 + y 2 ) 2 = 16x 2 – 9y 2
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