Answer:
(x-4)^2 + (y-5)^2 = 20
Step-by-step explanation:
Rearrange the line equation of 5x - 2y + 6 = 0
So y = 5/2x +3
The y-intercept of the line equation is 3 as when x=0, y=3.
We know the Circle has the formula [tex](x-4)^2 + (y-5)^2 = ?^2[/tex] from the question but with the intercept, we can find the entire equation as the y-intercept is (0,3) so we can substitute it into the equation to find the full equations so:
[tex](0-4)^2 + (3-5)^2 = ?^2[/tex]
This simplifies to:
[tex](-4)^2 +(-2)^2[/tex] = [tex]?^2[/tex]
16 + 4 = 20 = [tex]?^2[/tex]
The answer is 20 so the equation of the circle is [tex](x-4)^2 + (y-5)^2 = 20[/tex]
