Question

The circle represented by the equation

$x ^ { 2 } + y ^ { 2 } + 2 g x + 2 f y + c = 0$ will be a point circle, if .

• A. $g ^ { 2 } + f ^ { 2 } = c$
• B. $g ^ { 2 } + f ^ { 2 } > c$
• C. $g ^ { 2 } + f ^ { 2 } + c = 0$
• D. None of these

Answer 1

Answer: (A)

$g ^ { 2 } + f ^ { 2 } = c$

Answer 2

Using condition of point circle

$R = \sqrt { g ^ { 2 } + f ^ { 2 } - c } = 0 \Rightarrow g ^ { 2 } + f ^ { 2 } = c$.