Question

Step by step please.

Answer 1

Ok so the general form of a circle is given by;

(x-a)²+(y-b)²=r²

where a and b are the coordinates of the center

and r is the radius of the circle

For this case we know that the center is (5,-7)

So the general equation of the circle would be;

`(x - 5) {}^(2) + (y - ( - 7)) {}^(2) = r {}^(2)`

`(x - 5 {}^(2) + (y + 7) {}^(2) = r {}^(2)`

Since we know that (-3,-1) is a point on that circle, we can say that it satisfies the equation of the circle;

`( - 3 - 5) {}^(2) + ( - 1 + 7) {}^(2) = r {}^(2)`

`r {}^(2) = ( - 8) {}^(2) + ( 6) {}^(2)`

`r {}^(2) = 64 + 36 = 100`

So now,

`(x - 5) {}^(2) + ( {y + 7)}^(2) = 100`