Question

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

Answer 1

$Letradius=r$

$e{q}^{n}ofcircle$ with center$(r,0)$

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

$x^2-2rx+r^2+y^2=r^2$

$x^2+y^2-2rx=0$

$circlepassesthrough(3,4)$

$3^2+4^2-2r\times 3=0$

$25=6r$

$\therefore r=\left(\frac{25}{6}\right)$

$\therefore e{q}^{n}ofcircle$
$x^2+y^2-\left(\frac{25x}{3}\right)=0$

$or3x^2+3y^2-25x=0$