Question

The center of a circle is $(2a-1,7)$ and it passes through the point $(-3,-1)$. If the diameter of the circle is $20$ units, then find the value of $a$.

Answer 1

Centre: $C(2a-1,7)$

Point: $P(-3,-1)$

Radius=$\frac{1}{2}\left(20\right)=10$

As circle passes through P, distance between p and centre is equal to radius.

=>${\left(PC\right)}^2=(10{)}^2=>(2a-1+3{)}^2+{(7+1)}^2=(10{)}^2=>(a+1{)}^2=\frac{36}{4}=>(a+1{)}^2=9=>a=2,-4$