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
- A \(\left(\frac{5}{4}, \frac{5}{2}\right)\)
- B \((5,-5)\)
- C \((10,-5 \sqrt{2})\)
- D \(\left(\frac{5}{2}, \frac{5 \sqrt{2}}{2}\right)\)
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, \(2at_1 > 0 \Rightarrow t_1 > 0\))…
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