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TS EAMCET · Maths · Parabola

A normal chord PQ drawn at a point P on the parabola \(y^2=5 x\) subtends a right angle at the vertex. If P lies in the first quadrant, then the other end Q of the normal chord is

  1. A \(\left(\frac{5}{4}, \frac{5}{2}\right)\)
  2. B \((5,-5)\)
  3. C \((10,-5 \sqrt{2})\)
  4. D \(\left(\frac{5}{2}, \frac{5 \sqrt{2}}{2}\right)\)
Verified Solution

Answer & Solution

Correct Answer

(C) \((10,-5 \sqrt{2})\)

Step-by-step Solution

Detailed explanation

\(a = \frac{5}{4}\) \(t_1t_2 = -4\) \(t_2 = -t_1 - \frac{2}{t_1}\) \(t_1\left(-t_1 - \frac{2}{t_1}\right) = -4\) \(-t_1^2 - 2 = -4 \Rightarrow t_1^2 = 2\) \(t_1 = \sqrt{2}\) (since P is in first quadrant, \(2at_1 > 0 \Rightarrow t_1 > 0\))…