The locus of the centres of the circles, which touch the circle, x2 + y2 = 1 externally, also touch the y-axis and lie in the first quadrant, is

Engineering

Mathematics

A Circle

Locus of a Point

Line and Circle

Question

The locus of the centres of the circles, which touch the circle, x² + y² = 1 externally, also touch the y-axis and lie in the first quadrant, is

$x = \sqrt{1 + 2 y}, y \geq 0$

$y = \sqrt{1 + 2 x}, x \geq 0$

$x = \sqrt{1 + 4 y}, y \geq 0$

$y = \sqrt{1 + 4 x}, x \geq 0$

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$\sqrt{h^{2} + k^{2}} = | h | + 1$

⇒ x² + y² = x² + 1 – 2x

⇒ y² = 1 + 2x

$\Rightarrow y = \sqrt{1 + 2 x}; x \geq 0$