Question

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

• A. $x^2+y^2-5x=0$
• B. $2x^2+2y^2-5x=0$
• C. $x^2+y^2+5x=0$
• D. $x^2-y^2-5x=0$

Answer 1

The correct option is B $2x^2+2y^2-5x=0$

Let the equation of required circle is $x^2+y^2+2gx+2fy+c=0$

It passes through origin $⟹c=0$

it touches $y-axis⟹f^2=c⟹f=0$

It passes through $(2,1)⟹2^2+1^2+2g\left(2\right)+2\left(0\right)\left(2\right)+0=04g=-5g=\frac{-5}{4}$

Substituing the values of $g,f,c$

The equation is $2x^2+2y^2-5x=0$