If (-4, 11) and (-6,5) are the endpoints of a diameter of a circle, what is the equation of the circle?

The equation of the circle is given as:

Solution:

Given that,

(−4, 11) and (−6, 5) are the endpoints of a diameter of a circle

The standard form of the equation of a circle is:

Where,

(a, b) are the co-ordinates of the centre and r is the radius

To find the centre:

Find the midpoint of two given points

calculate the radius using the  distance formula

Distance between center and one end point = radius

(-5, 8) and (-4, 11)

The equation of the circle is given as:

Thus the equation of circle is found