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lora16 [44]
3 years ago
7

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

Mathematics
1 answer:
Volgvan3 years ago
4 0

Answer:

If you've more doubts you can ask :)

Step-by-step 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

<em><u>First we will find the centre, (a , b): </u></em>

<em><u /></em>a = \frac{3+(-1)}{2} = \frac{2}{2} = 1\\\\b = \frac{-2 + 4}{2} = \frac{2}{2} = 1<em><u /></em>

<em><u>Find radius:</u></em>

Radius, r = \frac{Diameter}{2}

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

diameter = \sqrt{(x_2 - x_1)^2 +(y_2-y_1)^2} \\\\

             = \sqrt{(3-(-1)^2 + (-2-4)^2} \\\\=\sqrt{16 + 36}\\\\=\sqrt{52}\\\\=\sqrt{4 \times 13}\\\\=2\sqrt{13}    \ units

Therefore , r = \frac{2 \times \sqrt{13} }{2} = \sqrt{13}  \ units

<em><u>Equation of the circle is :  </u></em>

                                 (x - 1)^2 +(y-1)^2 = 13<em><u></u></em>

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