Question

Find the equations of the circles touching y-axis at (0, 3) and making an intercept of 8 units on the x-axis.

Answer 1

The circle touches y - axis at C(0 3) and makes an intercept AB of B units on x-axis.
$\therefore AB=8$
Let M be the mid-point of AB
We know OM = 3 and AM = 4
$(\because AM=\frac{1}{2})$
$\therefore$ In $\Delta AOM$
$A{O}^2=A{M}^2+M{O}^2=4^2+3^2=25\therefore AO=5$
Also, AO = CO = 5 (radius)
$\therefore$ centre = 0 (5, 3)
Thus, the equation of circle is
$(x-5{)}^2+(y-3{)}^2=5^2\Rightarrow x^2+y^2\pm 10x-6y+9=0$