Question

I need help pleaseee!!

Answer 1

Answer:

(x - [-1])² + (y - [-1])² = [13]

Step-by-step 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 = $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

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

Center of the circle = $(\frac{-4+2}{2},\frac{-3+1}{2} )$

                                = (-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 = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Radius of the circle = $\sqrt{(-1-2)^2+(-1-1)^2}$

                                = $\sqrt{9+4}$

                                = $\sqrt{13}$

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]