JEE Main · 2019 · 12 Apr 2019 · Shift 2 · Circle

A circle touching the

x

-axis at

(3, 0)

and making an intercept of length 8 on the

y

-axis passes through the point :

(A) $(3, 5)$
(B) $(1, 5)$
(C) $(3, 10)$ ✓ Correct
(D) $(2, 3)$

Answer: (C)

Solution

Touching the

x

-axis at

(3, 0)

puts the centre at

(3, r)

with radius

r

. Setting

x = 0

(x - 3)^{2} + (y - r)^{2} = r^{2}

leaves a

y

-axis chord of length

2 r^{2} - 9

, and this equals

8

, so

r^{2} - 9 = 16

and

r = 5

. The circle is centred at

(3, 5)

with radius

5

, and

(3, 10)

, sitting directly above the centre at distance

5

, lies on it.

JEE Main · 2019 · 12 Apr 2019 · Shift 2 · Single correct option

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