Question

Write the equation of the circle passing through (3, 4) and touching y-axis at the origin.

Answer 1

It is given that the circle touches the y-axis at the origin.
Thus, the centre of the circle is (h,0) and its radius is h.
Hence, the equation of the circle is \[\left( x - h \right)^2 + \left( y \right)^2 = h^2\] i.e.

\[x^2 + y^2 - 2xh = 0\].

Also, the circle passes through (3, 4).

∴ \[25 - 6h = 0 \Rightarrow h = \frac{25}{6}\]

Hence, the required equation of the circle is \[\left( x - \frac{25}{6} \right)^2 + y^2 = \left[ \frac{25}{6} \right]^2\], i.e. 

\[3\left( x^2 + y^2 \right) - 25x = 0\].