TS EAMCET · Maths · Hyperbola
The locus of the mid-points of the chords of the circle \(x^2+y^2=16\) which are tangents to the hyperbola \(9 x^2-16 y^2=144\) is
- A \(12 x^2-8 y^2=x^2+y^2\)
- B \(9 x^2+12 y^2=\left(x^2+y^2\right)^2\)
- C \(16 x^2-9 y^2=\left(x^2+y^2\right)^2\)
- D \(16 x^2-6 y^2=x^4+y^4\)
Answer & Solution
Correct Answer
(C) \(16 x^2-9 y^2=\left(x^2+y^2\right)^2\)
Step-by-step Solution
Detailed explanation
Let \((h, k)\) be the mid-point of the chord of the circle \(x^2+y^2=16\), so that its equation by \(T=S_I\) is \[ h x+k y=h^2+k^2 \text { or } y=\frac{-h}{k} x+\frac{h^2+k^2}{k} \] It will touch the hyperbola if…
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