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Question: The locus of the centre of a circle which touches externally the circle x<sup>2</sup> + y<sup>2</sup...

The locus of the centre of a circle which touches externally the circle x2 + y2 – 6x – 6y + 14 = 0 and also touches the y-axis is given by the equation –

A

x2 – 6x – 10y + 14 = 0

B

x2 – 10x – 6y + 14 = 0

C

y2 – 6x – 10y + 14 = 0

D

y2 – 10x – 6y + 14 = 0

Answer

y2 – 10x – 6y + 14 = 0

Explanation

Solution

x2 + y2 – 6x – 6y + 14 = 0 ...(1)

Ž C1(3, 3) , r1 = 2

Locus of centre C2(h, k) = ?

Q C2N = r2 = |h| Ž C1C2 = (r1 + r2)

Q Both the circles touches each other externally.