JEE Main · 2019 · 11 Jan 2019 · Shift 1 · Circle

Two circles with equal radii intersecting at the points

(0, 1)

and

(0, - 1)

. The tangent at the point

(0, 1)

to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is:

(A)1
(B)2✓ Correct
(C) $22$
(D) $2$

Answer: (B)

Solution

The common chord joins

(0, 1)

and

(0, - 1)

, so it lies along the

y

-axis and the line of centres is the

x

-axis through the midpoint

(0, 0)

; place the centres at

(a, 0)

and

(- a, 0)

. Each circle passing through

(0, 1)

gives

r^{2} = a^{2} + 1

. The radius to

(0, 1)

from

(a, 0)

has slope

- \frac{1}{a}

, so the tangent there has slope

a

and equation

y = a x + 1

. Requiring this tangent to pass through the other centre

(- a, 0)

gives

0 = - a^{2} + 1

, so

a = 1

and the distance between centres is

2 a = 2

JEE Main · 2019 · 11 Jan 2019 · Shift 1 · Single correct option

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