Let the latus rectum of the parabola $y^{2}=4 x$ be the common chord to the circles $\mathrm{C}_{1}$ and $\mathrm{C}_{2}$ each of them having radius $2 \sqrt{5}$. Then, the distance between the centres of the circles $\mathrm{C}_{1}$ and $\mathrm{C}_{2}$ is:

JEE Main · 2020 · 03 Sep 2020 · Shift 2 · Parabola

Let the latus rectum of the parabola

y^{2} = 4 x

be the common chord to the circles

C_{1}

and

C_{2}

each of them having radius

25

. Then, the distance between the centres of the circles

C_{1}

and

C_{2}

is:

(A) $45$
(B) $85$
(C)8✓ Correct
(D)12

Answer: (C)

Solution

The latus rectum of

y^{2} = 4 x

is the chord

x = 1

running from

(1, 2)

(1, - 2)

, of length

4

. This chord is common to both circles, so each centre lies on its perpendicular bisector at a distance

r^{2} - 2^{2}

from the chord's midpoint, with

r = 25

and half-chord

2

. That distance is

20 - 4 = 4

. The two centres lie on opposite sides of the chord, so they are

2 \times 4 = 8

apart.

JEE Main · 2020 · 03 Sep 2020 · Shift 2 · Single correct option

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