AP EAMCET · Maths · Hyperbola
The locus of the mid-points of the chords of the circle \(x^2+y^2=16\) which are the tangents to the hyperbola \(9 x^2-16 y^2=144\) is
- A \(3 x^2-4 y^2=16\left(x^2+y^2\right)\)
- B \(4 x^2-3 y^2=9\left(x^2+y^2\right)\)
- C \(16 x^2-9 y^2=\left(x^2+y^2\right)^2\)
- D \(16 x^2-9 y^2=4\left(x^2+y^2\right)\)
Answer & Solution
Correct Answer
(C) \(16 x^2-9 y^2=\left(x^2+y^2\right)^2\)
Step-by-step Solution
Detailed explanation
Equation of chord with mid-point \((h, k)\) to the circle \(x^2+y^2=16\) is \(T=S_1\) \[ \begin{gathered} h x+k y-16=h^2+k^2-16 \\ y=-\frac{h}{k} x+\left(\frac{h^2+k^2}{k}\right) \end{gathered} \] For hyperbola \(9 x^2-16 y^2=144\)…
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