Let P and Q be distinct points on the parabola y 2 = 2 x   such that a circle with P Q as diameter passes through the vertex O of the parabola. If P lies in the first quadrant and the area of the triangle Δ O P Q is 3 2 ,   then which of the following is (are) the coordinates of P ?

Question

Let P and Q be distinct points on the parabola y 2 = 2 x &#160; such that a circle with P Q as diameter passes through the vertex O of the parabola. If P lies in the first quadrant and the area of the triangle &#916; O P Q is 3 2 , &#160; then which of the following is (are) the coordinates of P ?

Aicharya · Accepted Answer

∆ = 3 2 1 2 0 0 t 1 2 2 t 1 t 2 2 2 t 2 0 0 1 2 t 1 2 t 2 2 - t 2 2 t 1 2 = ± 3 2 1 4 t 1 t 2 t 1 - t 2 = ± 3 2 t 1 t 2 t 1 - t 2 = ± 12 2 t 1 - t 2 = ± 3 2 ⇒ t 1 - t 2 = 3 2 (as t 1 > t 2 ) t 1 + t 2 = 18 - 16 = ± 2 2 t 1 = 3 2 + 2 t 1 = 2 2 2 t 1 = 2 2 t 1 = 2 P 4 , 2 2 and P 1 , 2

Let P and Q be distinct points on the parabola y 2 = 2 x   such that a circle with P Q as diameter…

Solution

Let P and Q be distinct points on the parabola y 2 = 2 x &#160; such that a circle with P Q as diameter…

Solution

Let P and Q be distinct points on the parabola y 2 = 2 x such that a circle with P Q as diameter…