AP 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 \(8 x^2-9 y^2=\left(x^2+y^2\right)^2\)
- B \(16 x^2-9 y^2=\left(x^2+y^2\right)^2\)
- C \(9 x^2-14 y^2=\left(x^2+2 y^2\right)^2\)
- D \(3 x^2+4 y^2=\left(x^2+2 y^2\right)^2\)
Answer & Solution
Correct Answer
(B) \(16 x^2-9 y^2=\left(x^2+y^2\right)^2\)
Step-by-step Solution
Detailed explanation
Hyperbola: \(\frac{x^2}{16} - \frac{y^2}{9} = 1 \implies a^2=16, b^2=9\) Chord midpoint: \((h,k)\). Chord equation for \(x^2+y^2=16\): \(xh+yk=h^2+k^2\) Rewrite chord as \(y = -\frac{h}{k}x + \frac{h^2+k^2}{k}\). So \(m=-\frac{h}{k}, c=\frac{h^2+k^2}{k}\) Tangency condition for…
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