Question

The locus of the centres of the circles, which touch the circle, $x^2+y^2=1$ externally also touch the y-axis and lie in the first quadrant is:

• A. $y=\sqrt{1+4x},x\ge 0$
• B. $x=\sqrt{1+4y},y\ge 0$
• C. $x=\sqrt{1+2y},y\ge 0$
• D. $y=\sqrt{1+2x},x\ge 0$

Answer 1

The correct option is D $y=\sqrt{1+2x},x\ge 0$

$\sqrt{h^2+k^2}=\left|h\right|+1$
$\Rightarrow x^2+y^2=x^2+1+2x\Rightarrow y^2=1+2x\Rightarrow y=\sqrt{1+2x};x\ge 0$