Question

Radius of a circle passing through the origin and touching the parabola y² = 4x at (1, 2) is

• A. $\frac{5}{6}$
• B. $\frac{5\sqrt{2}}{6}$
• C. $\frac{5}{\sqrt{2}}$
• D. None of these

Answer 1

Answer: (C)

$\frac{5}{\sqrt{2}}$

Answer 2

Equation of normal at the point (1, 2) w.r.t. the parabola

y² = 4x is x + y –3 = 0.

Let the centre of the circle be (α, β) ⇒ α + β – 3 = 0. …. (1)

Also (α –1)² + (β –2)² = α² + β² i.e 2α + 4β = 5.

From (1) and (2), α = 7/2 and β = –1/2.