AP EAMCET · Maths · Circle
If the chord of contact of \(\mathrm{P}\left(x_1, y_1\right)\) with respect to the circle \(x^2+y^2=a^2\) meets the circle at \(\mathrm{A}\) and \(\mathrm{B}\); and if \(\lfloor \mathrm{AOB}=90^{\circ}\), then \(x_1^2+y_1^2=\)
- A \(a^2\)
- B \(2 a^2\)
- C \(3 a^2\)
- D \(4 a^2\)
Answer & Solution
Correct Answer
(B) \(2 a^2\)
Step-by-step Solution
Detailed explanation
Chord of contact AB: \(x x_1 + y y_1 = a^2\) Homogenizing equation of circle: \(x^2+y^2 = a^2 \left( \frac{x x_1 + y y_1}{a^2} \right)^2\) \(a^2(x^2+y^2) = (x x_1 + y y_1)^2\) \((a^2 - x_1^2)x^2 - 2x_1 y_1 xy + (a^2 - y_1^2)y^2 = 0\) For \(\lfloor AOB = 90^{\circ}\), coefficient…
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