TS EAMCET · Maths · Parabola
\(A(-2,3)\) is a fixed point outside the parabola \(y^2=4 a x(a>0)\) and \(P\) is a point moving on the parabola. The locus of point \(Q\) which divides \(A P\) in the ratio \(3: 2\) is a conic. Then focus of that conic is
- A \((a, 0)\)
- B \(\left(\frac{-4}{5}+\frac{3 a}{5}, \frac{a}{5}\right)\)
- C \(\left(\frac{3 a-4}{5}, \frac{6}{5}\right)\)
- D \(\left(\frac{a}{5}, \frac{3 a-4}{5}\right)\)
Answer & Solution
Correct Answer
(C) \(\left(\frac{3 a-4}{5}, \frac{6}{5}\right)\)
Step-by-step Solution
Detailed explanation
Let \(P\) be \(\left(a t^2, 2 a t\right)\) and \(Q\) be \((h, k)\). Also given, \(A=(-2,3)\) Now, since \(Q\) divides \(A P\) in the ratio \(3: 2\) i.e., \( \frac{A Q}{Q P}=\frac{3}{2} \)…
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