TS EAMCET · Maths · Parabola
If the locus of a point which divides a chord with slope 2 of the parabola \(y^2=4 x\), internally in the ratio \(1: 3\) is a parabola, then its vertex is
- A \((2,1)\)
- B \(\left(\frac{3}{16}, \frac{3}{2}\right)\)
- C \(\left(\frac{3}{4}, \frac{3}{16}\right)\)
- D \(\left(\frac{3}{16}, \frac{3}{4}\right)\)
Answer & Solution
Correct Answer
(D) \(\left(\frac{3}{16}, \frac{3}{4}\right)\)
Step-by-step Solution
Detailed explanation
Let \(P\left(t_1^2, 2 t_1\right)\) and \(Q\left(t_2^2, 2 t_2\right)\) are extremetre of chord \( \therefore \quad h=\frac{3 t_1^2+t_2^2}{4}, k=\frac{6 t_1+2 t_2}{4} \) Slope of \(P Q=2\)…
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