A circle has a center that falls on the line $y = 1/7x +4$ and passes through $( 7 ,8 )$ and $(3 ,6 )$ . What is the equation of the circle?

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A circle has a center that falls on the line $y = 1/7x +4$ and passes through $( 7 ,8 )$ and $(3 ,6 )$ . What is the equation of the circle?

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Answer 1 · 2018-04-23T15:36:58

$color(blue)((x-91/15)^2+(y-73/15)^2=481/45)$

Explanation:

The equation of a circle is given by:

$(x-h)^2+(y-k)^2=r^2$

Where $(h,k)$ are the $x and y$ coordinates of the centre respectively and $r$ is the radius.

The centre lie on the line $y=1/7x+4$

$:.$

$k=1/7h+4 \ \ \ \ \ \ [1]$

$(7,8) and (3,6)$ lie on the circle:

$(7-h)^2+(8-k)^2=r^2 \ \ \ \ \ \ [2]$

$(3-h)^2+(6-k)^2=r^2 \ \ \ \ \ \ [3]$

Subtract $[3]$ from $[2]$

$68-8h-4k=0$

Substituting $k=1/7h+4$

$68-8h-4(1/7h+4)=0$

$52-60/7h=0=>h=91/15$

Substituting in $[1]$ :

$k=1/7(91/15)+4$

$k=73/15$

We now need the value of $r^2$

Using coordinate $(3,6)$

$(3-91/15)^2+(6-73/15)^2=r^2$

$r^2=481/45$

So the equation of the circle is:

$color(blue)((x-91/15)^2+(y-73/15)^2=481/45)$

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A circle has a center that falls on the line $y = 1/7x +4$ and passes through $( 7 ,8 )$ and $(3 ,6 )$ . What is the equation of the circle?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

A circle has a center that falls on the line y = 1/7x +4 y = 1/7x +4 and passes through ( 7 ,8 ) ( 7 ,8 ) 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 $y = 1/7x +4$ and passes through $( 7 ,8 )$ and $(3 ,6 )$ . What is the equation of the circle?