Write The Following Equation Of The Circle In General Form That Will Satisfy The Given Conditions 1. The Line Segment Joining (0,7) Anf (-6,-3) Is A D

write the following equation of the circle in general form that will satisfy the given conditions 1. the line segment joining (0,7) anf (-6,-3) is a diameter.

 

Answer:

(x + 3)² + (y - 2)² = (√34)²               (standard form)

x² + y² + 6x - 4y -21 = 0                  (general form)

Step-by-step explanation:

write the following equation of the circle in general form that will satisfy the given conditions 1. the line segment joining (0,7) anf (-6,-3) is a diameter.

use midpoint formula to determine the center of the circle

use distance formula to determine the diameter and radius of the circle

Center:

( (0 + -6)/2 , (7 + -3)/2 ) = (-3 , 2)

Radius:

d = √ (x2 - x1)² + (y2 - y1)² = √ (-6 - 0)² + (-3 - 7)²  = 2√34

r = 0.5d = 0.5(2√34) = √34

Equation of the circle:

(x + 3)² + (y - 2)² = (√34)²               (standard form)

x² + y² + 6x - 4y -21 = 0                  (general form)