Answer:
Equation of the circle: [tex]x^2 + y^2 +4x -8y +2 = 0[/tex]
Step-by-step explanation:
Given:
[tex]r = 3\sqrt{2} \\C(-2, 4)[/tex]
Find:
Equation of the Circle= ?
Solution:
Standard form of Circle:
[tex](x-h)^{2} + (y-k)^{2} = r^{2}[/tex]
The General form of Circle:
[tex]x^2 + y^2 + Dx + Ey + F = 0[/tex]
where D, E and F are constants.
since we are given the points (or coordinates of the circle):
C(h, k) = C(-2, 4)
We can substitute the values of h, k and the radius in the standard form:
[tex][x-(-2)]^{2} + [y- (4)]^{2} = (3\sqrt{2} )^2\\(x+2)^{2} + (y-4)^{2} = 18\\(x^{2} +2x + 2x +4) +(y^2 -4y - 4y +16) = 18\\(x^2 +4x+4) + (y^2 -8y + 16)=18\\[/tex]
Combine like terms:
[tex]x^2 + y^2+4x -8y + 4+16-18 = 0\\\\x^2 +y^2 +4x-8y +2 = 0[/tex]← (This is the equation of the circle)
