Question

If the circle $x ^ { 2 } + y ^ { 2 } + 2 g x + 2 f y + c = 0$ touches x-axis, then.

• A. $g = f$
• B. $g ^ { 2 } = c$
• C. $f ^ { 2 } = c$
• D. $g ^ { 2 } + f ^ { 2 } = c$

Answer 1

Answer: (B)

$g ^ { 2 } = c$

Answer 2

Touches x-axis, hence radius = ordinate of centre.

Hence $\sqrt { g ^ { 2 } + f ^ { 2 } - c } = ( - f )$ or $g ^ { 2 } = c$.