Question

The equation of the circle which touches the axis of $y$ at the origin and passes through $(3,4)$ is-

• A. $4(x^2+y^2)-25x=0$
• B. $3(x^2+y^2)-25x=0$
• C. $2(x^2+y^2)-3x=0$
• D. $4(x^2+y^2)-25x+10=0$

Answer 1

The correct option is B $3(x^2+y^2)-25x=0$

The center of the circle lies on the x-axis
Let $a$ be the radius of the circle, then coordinate of the center are $(a,0)$

The circle passes through $(3,4)$ , therefore

$\sqrt{{(a-3)}^2+{(0-4)}^2}=a\Rightarrow -6a+25=0\Rightarrow a=\frac{25}{6}$

So, the equation of the circle is

${(x-a)}^2+{(y-0)}^2=a^2$

$\Rightarrow x^2+y^2-2ax=0$

$\Rightarrow 3(x^2+y^2)-25x=0$