Find the standard form of the equation of the circle with endpoints of a diameter at the points (3,8) and (-7,2)

+= 34

The equation of a circle in standard form is

+=

where (a , b) are the coordinates of the centre and r is the radius

The centre is at the midpoint of the endpoints and the radius is the distance from the centre to either of the 2 endpoints

Using the midpoint formula

midpoint = [(x+, (+

where (,=(3,8) and (,=(-7,2)

centre = ((3-7),(8+2)) = (-2,5)

Calculate r using the distance formula

r = √(-)²+(-)²)

= √((3+2)²+(8-5)²) = √(25+9) = √34 ⇒ r² =(√34)² = 34

equation of circle is : (x+2)²+(y-5)² = 34

answer:

your answer is: c. 196 7/8 in^3.