A circle has a center that falls on the line $y = 1/8x +4$ and passes through $( 5 ,8 )$ and $(5 ,6 )$ . What is the equation of the circle?

Question

1688 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-22T10:21:43

$(x-24)^2+(y-7)^2=362$

Using the two given points $(5, 8)$ and $(5, 6)$

Let $(h, k)$ be the center of the circle

For the given line $y=1/8x+4$ , $(h, k)$ is a point on this line.
Therefore, $k=1/8h+4$

$r^2=r^2$

$(5-h)^2+(8-k)^2=(5-h)^2+(6-k)^2$

$64-16k+k^2=36-12k+k^2$

$16k-12k+36-64=0$

$4k=28$

$k=7$

Use the given line $k=1/8h+4$

$7=1/8*h+4$

$h=24$

We now have the center $(h, k)=(7, 24)$

We can now solve for the radius r

$(5-h)^2+(8-k)^2=r^2$ (5-24)^2+(8-7)^2=r^2#

$(-19)^2+1^2=r^2$
$361+1=r^2$

$r^2=362$

Determine now the equation of the circle

$(x-h)^2+(y-k)^2=r^2$
$(x-24)^2+(y-7)^2=362$

The graphs of the circle $(x-24)^2+(y-7)^2=362$ and the line $y=1/8x+4$

graph{((x-24)^2+(y-7)^2-362)(y-1/8x-4)=0[-55,55,-28,28]}

God bless....I hope the explanation is useful.

A circle has a center that falls on the line y = 1/8x +4 y = 1/8x +4 and passes through ( 5 ,8 ) ( 5 ,8 ) and (5 ,6 )(5 ,6 ). What is the equation of the circle?