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k0ka [10]
3 years ago
8

The endpoints of a diameter of a circle are (5,-10) and (-7,2). What is the equation of the circle in standard form?

Mathematics
1 answer:
grin007 [14]3 years ago
5 0

Answer:

(x+1)^2+(y+4)^2=(6\sqrt{2})^2

Step-by-step explanation:

The length of the diameter(d) will be the distance between (5,-10)\ and\ (-7,2).

d=\sqrt{(2-(-10))^2+(-7-5)^2}=\sqrt{(12)^2+(-12)^2}=\sqrt{144+144}=\sqrt{288}\\\\d=12\sqrt{2}

Radius:

radius(r)=\frac{diameter}{2}=\frac{12\sqrt{2}}{2}=6\sqrt{2}

Centre:

Let (a,b) be centre of the circle.

Centre will be the mid point of end points of diameter.

a=\frac{5-7}{2}=\frac{-2}{2}=-1\\\\b=\frac{-10+2}{2}=\frac{-8}{2}=-4\\\\Centre=(-1,-4)

Equation of circle:

If (a,b) be centre and r be the radius.

Equation of circle: (x-a)^2+(y-b)^2=r^2

Here (a,b)=(-1,-4)\ and\ r=6\sqrt{2}

(x-(-1))^2+(y-(4))^2=(6\sqrt{2})^2\\(x+1)^2+(y+4)^2=(6\sqrt{2})^2

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\qquad\qquad\huge\underline{{\sf Answer}}

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\qquad \sf  \dashrightarrow \:y =  - 4x + 4

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