hello student,

Here is the solution.

So, the equation is

X^2+Y^2-4X+7Y =0 ---------------------------------------------------------------------------------------(I)

Radius = 4

We need to find a.

((X-2)^2-4)+((Y+3.5)^2-12.25)=0

(X-2)^2+(Y+3.5)^2 = 16.25 ----------------------------------------------------------------------------(1)

Since radius is given as 4, this 16.25 is rounded to 16

SO the actual equation is X^2+Y^2=R^2

Which is modified to:

(X-a)^2+(Y+b)^2 = R^2 ---------------------------------------------------------------------------------(2)

Comparing equation (1) with equaltion (2)

R= 4,

a=2

Therefore a=2