Question

I need help pleaseee!!

Answer 1

(x - [-1])² + (y - [-1])² = [13]

Explanation:

If P and Q are the end-points of the diameter PQ, midpoint of the segment PQ will be the center of the circle. (Definition of the center of a circle)

Midpoint of a segment having extreme ends
`(x_1, y_1)` and
`(x_2,y_2)`

Coordinates of the center =
`((x_1+x_2)/(2),(y_1+y_2)/(2))`

Since, extreme ends of the diameter are P(-4, -3) and Q(2, 1)

Center of the circle =
`((-4+2)/(2),(-3+1)/(2) )`

= (-1, -1)

Radius of the circle = Distance between the center and Q,

Since distance between the two points
`(x_1, y_1)` and
`(x_2,y_2)` is,

d =
`√((x_2-x_1)^2+(y_2-y_1)^2)`

Radius of the circle =
`√((-1-2)^2+(-1-1)^2)`

=
`√(9+4)`

=
`√(13)`

Equation of the circle will be,

(x - h)² + (y - k)² = r²

Where (h, k) is the center and 'r' is the radius of the circle,

(x - [-1])² + (y - [-1])² = [13]