JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
The locus of the midpoints of the chord of the circle, \(x^{2}+y^{2}=25\) which is tangent to the hyperbola \(, \frac{ x ^{2}}{9}-\frac{ y ^{2}}{16}=1\) is
- A \(\left(x^{2}+y^{2}\right)^{2}-16 x^{2}+9 y^{2}=0\)
- B \(\left(x^{2}+y^{2}\right)^{2}-9 x^{2}+144 y^{2}=0\)
- C \(\left(x^{2}+y^{2}\right)^{2}-9 x^{2}-16 y^{2}=0\)
- D \(\left(x^{2}+y^{2}\right)^{2}-9 x^{2}+16 y^{2}=0\)
Answer & Solution
Correct Answer
(D) \(\left(x^{2}+y^{2}\right)^{2}-9 x^{2}+16 y^{2}=0\)
Step-by-step Solution
Detailed explanation
\(y-k=-\frac{h}{k}(x-h)\) \(ky - k ^{2}=- hx + h ^{2}\) \(hx + ky = h ^{2}+ k ^{2}\) \(y =-\frac{ hx }{ k }+\frac{ h ^{2}+ k ^{2}}{ k }\) tangent to \(\frac{ x ^{2}}{9}-\frac{ y ^{2}}{16}=1\) \(c ^{2}= a ^{2} m ^{2}- b ^{2}\)…
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