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

y = - 6

step-by-step explanation:

given the point (- 2, y) lies on the graph then it is a solution of it's equation.

substitute x = - 2 into the equation for value of y

y = 3(- 2) = 3 × - 2 = - 6

the point on the graph is (- 2, 6)

24

step-by-step explanation: