Consider a family of circles which are passing through point (- 1, 1) and are tangent to x- axis. If

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10-1.Circle and System of Circles

hard

Consider a family of circles which are passing through the point $(- 1, 1)$ and are tangent to $x-$ axis. If $(h, k)$ are the coordinate of the centre of the circles, then the set of values of $k$ is given by the interval

A

$k \le \frac{1}{2}$

B

$k \ge \frac{1}{2}$

C

$ - \frac{1}{2} \le k \le \frac{1}{2}$

D

$0 < k < \frac{1}{2}$

(AIEEE-2007)

Solution

Equation of circle $(x-h)^{2}+(y-k)^{2}=k^{2}$

It is passing through $(-1,1)$ then $(-1-h)^{2}+(1-k)^{2}=k^{2}$

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

$D \geq 0$

$2 k-1 \geq 0 \Rightarrow k \geq 1 / 2$

Standard 11

Mathematics

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