1 Answer

Andrey Markeev · Answer 1 · 2021-03-11T17:05:46+0000

The equation of the circle is given as:

(x+5)^2 + (y-8)^2 = 10

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:

(x-a)^2 + (y-b)^2=r^2

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

m = ((x_1+x_2)/(2) , (y_1+y_2)/(2))

$m = ((-4-6)/( 2), (11+5)/(2))\\\\m = (-5, 8)$

calculate the radius using the distance formula

Distance between center and one end point = radius

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

d = √((x_2-x_1)^2 + (y_2-y_1)^2)

$d = √((-4+5)^2 + (11-8)^2)\\\\d = √(1 + 9)\\\\d = √(10)$

The equation of the circle is given as:

(x-a)^2 + (y-b)^2=r^2

$(x+5)^2 + (y-8)^2 = (√(10))^2\\\\(x+5)^2 + (y-8)^2 = 10$

Thus the equation of circle is found

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