question_answer

The equation of family of circles with centre at\[(h,\text{ }k)\]touching the\[x-\]axis is given by

A)  \[{{x}^{2}}+{{y}^{2}}-2hx+{{h}^{2}}=0\]

B)  \[{{x}^{2}}+{{y}^{2}}-2hx-2fy+{{h}^{2}}=0\]

C)  \[{{x}^{2}}+{{y}^{2}}-2hx-2ky-{{h}^{2}}=0\]

D)  \[{{x}^{2}}-{{y}^{2}}-2hx-2ky=0\]

E)  \[{{x}^{2}}+{{y}^{2}}+2hx+2ky=0\]

Correct Answer: B

Solution :

Let C (h, k) be the centre of the circle. Since, the circle touches theaxis,                             Hence, the equation of the circle is