Question

Please please help me

Answer 1

`\large\boxed{(x-5)^2+(y+7)^2=36}`

Explanation:

The equation of a circle in standard form:

`(x-h)^2+(y-k)^2=r^2`

(h, k) - center

r - radius

We hace the center at (5, -7) → h = 5 and k = -7.

The radius is equal to the distance petween the center and other point on the circumference of a circle.

The formula of a distance between two points:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

Substitute the coordinates of the points (5, -7) and (5, -1):

`d=√((5-5)^2+(-1-(-7))^2)=√(0^2+6^2)=√(36)=6`

Therefore the equation of a circle is:

`(x-5)^2+(y-(-7))^2=6^2\\\\(x-5)^2+(y+7)^2=36`