The locus of a centre of a circle which touches externally the circle $x^{2} + y^{2} - 6 x - 6 y + 14 = 0$ and also touches the y-axis is given by the equation

x^{2} - 6 x - 10 y + 14 = 0

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x^{2} - 10 x - 6 y + 14 = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

y^{2} - 6 x - 10 y + 14 = 0

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y^{2} - 10 x - 6 y + 14 = 0

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Solution

The correct option is D $y^{2} - 10 x - 6 y + 14 = 0$
let the center of the circle be $(h, k)$ and since it touches the y-axis
Therefore, its radius will be $h$

it touches the circle $x^{2} + y^{2} - 6 x - 6 y + 14 = 0$ externally

Therefore, $C_{1} C_{2} = r_{1} + r_{2}$

$\Rightarrow \sqrt{(h - 3)^{2} + (k - 3)^{2}} = h + 2$

$\Rightarrow k^{2} - 10 h - 6 k + 14 = 0$

$\Rightarrow y^{2} - 10 x - 6 y + 14 = 0$

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Similar questions

Q. The locus of the centre of a circle, which touches externally the circle

x^{2} + y^{2} - 6 x - 6 y + 14 = 0

and also touches the y-axis, is given by the equation

Q. The locus of the centre of a circle, which touches externally the circle

x^{2} + y^{2} - 6 x - 6 y + 14 = 0

and also touches the

y

-axis, is given by the equation

The locus of the centre of a circle which touches externally the circle, $x^{2} + y^{2} - 6 x - 6 y + 14 = 0$ and also touches the y-axis is given by the equation:

Q. The locus of the centre of the circle which touches externally the circle

x^{2} + y^{2} - 6 x - 6 y + 14 = 0

and also touches the

y

-axis is given by the equations

Q. The locus of the centre of a circle which touches the circle

x^{2} + y^{2} - 6 x - 6 y + 14 = 0

externally and touches the y-axis s given by:

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The locus of a 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

The correct option is D y2−10x−6y+14=0let the center of the circle be (h,k) and since it touches the y-axisTherefore, its radius will be hit touches the circle x2+y2−6x−6y+14=0 externallyTherefore, C1C2=r1+r2⇒√(h−3)2+(k−3)2=h+2⇒k2−10h−6k+14=0⇒y2−10x−6y+14=0

The locus of a centre of a circle which touches externally the circle $x^{2} + y^{2} - 6 x - 6 y + 14 = 0$ and also touches the y-axis is given by the equation