A circle has a center that falls on the line $y = 8/7x +2$ and passes through $( 2 ,1 )$ and $(3 ,6 )$ . What is the equation of the circle?

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A circle has a center that falls on the line $y = 8/7x +2$ and passes through $( 2 ,1 )$ and $(3 ,6 )$ . What is the equation of the circle?

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Answer 1 · 2016-11-06T19:52:14

$C(70/47,174/47)$ radius $=root2(16705/2209)$
Equation of circumference is $(x-70/47)^2+(y-174/47)^2=16705/2209$

Explanation:

$A(2,1)$ and $B(3,6)$ a point $C$ on the line $y=8/7x+2$ has coordinates $C(x,8/7x+2)$ .

The centre $C$ can be found by imposing that $AC=BC$

$root2((2-x)^2+(1-8/7x-2)^2)=root2((3-x)^2+(6-8/7x-2)^2)$
By squaring boh members we get

$4-4x+x^2+1+16/7x+64/49x^2=9-6x+x^2+16-64/7x+64/49x^2$
that properly manipulated becomes
$16/7x-4x+64/7x+6x=25-5$ from which
$x=70/47$ and consequently
$y=8/7*70/47+2=80/47+2=174/47$ .
These are the coordinates of the centre $C$
The squared radius is $R^2=(2-70/47)^2+(1-174/47)^2=16705/2209$

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A circle has a center that falls on the line $y = 8/7x +2$ and passes through $( 2 ,1 )$ and $(3 ,6 )$ . What is the equation of the circle?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

A circle has a center that falls on the line y = 8/7x +2 y = 8/7x +2 and passes through ( 2 ,1 ) ( 2 ,1 ) and (3 ,6 )(3 ,6 ). What is the equation of the circle?

1 Answer

Explanation:

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A circle has a center that falls on the line $y = 8/7x +2$ and passes through $( 2 ,1 )$ and $(3 ,6 )$ . What is the equation of the circle?