JEE Advanced | 2015CircleHard
Question
Let P and Q be distinct points on the parabola y2 = 2x such that a circle with PQ as diameter passesthrough the vertex O of the parabola. If P lies in the first quadrant and the area of the triangle ᐃOPQis 3√2, then which of the following is(are) the coordinates of P ?
Options
A.(4, 2√2)
B.(9,3√2)
C.
D.(1, √2)
Solution
∵ ⎳POQ =
⇒ t1t2 = - 4∴
= 6 √2⇒
= 6√2⇒ |t1 - t2| = 3√2
⇒ t1 +
= 3√2 (∵ t1 > 0)We get t1 = 2√2, √2
P(4, 2√2) or (1, √2)
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