JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
The locus of the centroid of the triangle formed by any point \(\mathrm{P}\) on the hyperbola \(16 \mathrm{x}^{2}-9 \mathrm{y}^{2}+\) \(32 x+36 y-164=0\), and its foci is:
- A \(9 x^{2}-16 y^{2}+36 x+32 y-36=0\)
- B \(16 x^{2}-9 y^{2}+32 x+36 y-36=0\)
- C \(16 x^{2}-9 y^{2}+32 x+36 y-144=0\)
- D \(9 x^{2}-16 y^{2}+36 x+32 y-144=0\)
Answer & Solution
Correct Answer
(B) \(16 x^{2}-9 y^{2}+32 x+36 y-36=0\)
Step-by-step Solution
Detailed explanation
Given hyperbola is \(16(x+1)^{2}-9(y-2)^{2}=164+16-36=144\) \(\Rightarrow \frac{(x+1)^{2}}{9}-\frac{(y-2)^{2}}{16}=1\) \(\text { Eccentricity, } e=\sqrt{1+\frac{16}{9}}=\frac{5}{3}\) \(\Rightarrow \text { foci are }(4,2) \text { and }(-6,2)\) Let the centroic be…
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