Question

If (-1,4) and (3,-2) are end points of diameter of the circle, then the equation of the circle is

Answer 1

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Explanation:

If the centre of a circle is (a, b) and radius r, then the equation of the circle is :

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

First we will find the centre, (a , b):

`a = (3+(-1))/(2) = (2)/(2) = 1\\\\b = (-2 + 4)/(2) = (2)/(2) = 1`

Find radius:

`Radius, r = (Diameter)/(2)`

Diameter is the distance between (-1, 4) and (3, -2)

`diameter = √((x_2 - x_1)^2 +(y_2-y_1)^2) \\\\`

`= √((3-(-1)^2 + (-2-4)^2) \\\\=√(16 + 36)\\\\=√(52)\\\\=√(4 * 13)\\\\=2√(13) \ units`

Therefore ,
`r = (2 * √(13) )/(2) = √(13) \ units`

Equation of the circle is :

`(x - 1)^2 +(y-1)^2 = 13`