Question

If the equation $x ^ { 2 } + y ^ { 2 } + 2 g x + 2 f y + c = 0$ represents a circle with x-axis as a diameter and radius a, then.

• A. $f = 2 a , g = 0 , c = 3 a ^ { 2 }$
• B. $f = 0 , g = a , c = 3 a ^ { 2 }$
• C. $f = 0 , g = - 2 a , c = 3 a ^ { 2 }$
• D. None of these

Answer 1

Answer: (C)

$f = 0 , g = - 2 a , c = 3 a ^ { 2 }$

Answer 2

Here $\sqrt { f ^ { 2 } + g ^ { 2 } - c } = a$

f must be zero; $\Rightarrow g ^ { 2 } - c = a ^ { 2 }$.