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  • A circle touches the -axis and also touches the circle with center at <img alt="(4,0)" src="https://entrancecorner.oncod

A circle touches the y -axis and also touches the circle with center at (4,0) and radius 3 . The locus of the center of the circle is

Option: 1

a circle


Option: 2

 an ellipse


Option: 3

 a parabola


Option: 4

a hyperbola


Answers (1)

\mathrm{CC}_{1}=\mathrm{h}+3

(\mathrm{h}-4)^{2}+\mathrm{k}^{2}=(\mathrm{h}+3)^{2}
\mathrm{k}^{2}-8 \mathrm{~h}+16=6 \mathrm{~h}+9
\Rightarrow \mathrm{k}^{2}-14 \mathrm{~h}+7=0

\text{Required locus of}\: \mathrm{C}(\mathrm{h}, \mathrm{k})$ is $\mathrm{y}^{2}=14\left(x-\frac{1}{2}\right)

Posted by

Ramraj Saini

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