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Locus of the centre of the circle which ...

Locus of the centre of the circle which touches `x^2+y^2 - 6x-6y+14 =0` externally and also y-axis is:

A

`x^(2)-6x-10y-14=0`

B

`x^(2)-10x-6y-14=0`

C

`y^(2)-6x-10y+14=0`

D

`y^(2)-10x-6y+14=0`

Text Solution

Verified by Experts

The correct Answer is:
4
Let the center of the variable circles be (h,k).
Since the circel touches the axis of y, its radius is `|h|`.
The radius of the circle `x^(2)+y^(2)-6x-6y+14=0` is 2 and its center at (3,3)
Since the two circles touch each other externally.
Distance between the centers `=` Sum of the radii
or `sqrt((h-3)^(2)+(k-3)^(2))=|h| +2 `
or `k^(2)-10h-6k+14=0` (Considering `hgt0)`
Hence, the locus `(h,k)` is `y^(2)-10x-6y+14=0`.
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