JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 · Circle

Consider the circle

x^{2} + y^{2} = 9

and the parabola

y^{2} = 8 x

. They intersect at

P

and

Q

in the first and the fourth quadrants, respectively. Tangents to the circle at

P

and

Q

intersect the

x

-axis at

R

and tangents to the parabola at

P

and

Q

intersect the

x

-axis at

S

.

The radius of the circumcircle of the triangle

P R S

(A)5
(B) $33$ ✓ Correct
(C) $32$
(D) $23$

Answer: (B)

Solution

Points:

P = (1, 22)

R = (9, 0)

S = (- 1, 0)

.

The circumcircle passes through these three points. Its equation is of the form:

(x + 1) (x - 9) + y^{2} + λ y = 0

Substituting

P = (1, 22)

(1 + 1) (1 - 9) + 8 + 22 λ = 0

- 16 + 8 + 22 λ = 0

λ = 22

Circumcircle:

x^{2} + y^{2} - 8 x + 22 y - 9 = 0

Radius:

r = 16 + 2 + 9 = 27 = 33

JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 · Single correct option

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