Question:
Find the equation of a circle with Centre $(2,4)$ and radius 5
Solution:
The general form of the equation of a circle is:
$(x-h)^{2}+(y-k)^{2}=r^{2}$
Where, (h, k) is the centre of the circle.
r is the radius of the circle.
Substituting the centre and radius of the circle in he general form:
$\Rightarrow(x-2)^{2}+(y-4)^{2}=5^{2}$
$\Rightarrow(x-2)^{2}+(y-4)^{2}=25$
Ans; equation of a circle with Centre (2, 4) and radius 5 is:
$\Rightarrow(x-2)^{2}+(y-4)^{2}=25$