Question

The equation of the circle passing through the point (2, 1) and touching y-axis at the origin is.

• A. $x ^ { 2 } + y ^ { 2 } - 5 x = 0$
• B. $2 x ^ { 2 } + 2 y ^ { 2 } - 5 x = 0$
• C. $x ^ { 2 } + y ^ { 2 } + 5 x = 0$
• D. None of these

Answer 1

Answer: (B)

$2 x ^ { 2 } + 2 y ^ { 2 } - 5 x = 0$

Answer 2

We have the equation of circle

$x ^ { 2 } + y ^ { 2 } + 2 g x + 2 f y + c = 0$

But it passes through (0, 0) and (2, 1), then

$c = 0$ ….(i)

$5 + 4 g + 2 f = 0$ ….(ii)

Also $\sqrt { g ^ { 2 } + f ^ { 2 } - c } = | g |$ ⇒ $f = 0$ $\{ \because c = 0 \}$

From (ii), $g = - \frac { 5 } { 4 }$

Hence the equation will be $2 x ^ { 2 } + 2 y ^ { 2 } - 5 x = 0$ .