SOLUTION: Center at (-4,3), tangent to the line y= -4x-30

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Question 1040552: Center at (-4,3), tangent to the line y= -4x-30
Found 3 solutions by josgarithmetic, Edwin McCravy, ikleyn:
Answer by josgarithmetic(39615) About Me  (Show Source):
You can put this solution on YOUR website!
The tangent line is perpendicular to a radius. You want to know the line's equation having slope 1%2F4 passing through the given center (-4,3). This is y-3=%281%2F4%29%28x%2B4%29
y-3=x%2F4%2B1
y=x%2F4%2B4


A point ON the circle is the intersection of system%28y=x%2F4%2B4%2Cand%2Cy=-4x-30%29.

How far is this intersection from the center of the circle (-4,3)?
Distance Formula, giving this radius.

Do still need more help?

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

A better way is to use the formula for the distance from
a point to a line.  Here's that way:




The distance from the point (x1,y1)
to the line Ax+By+C=0 is given by the formula:

d%22%22=%22%22abs%28%28Ax%5B1%5D%2BBy%5B1%5D%2BC%29%2Fsqrt%28A%5E2%2BB%5E2%29%29

The line y= -4x-30 is the line 4x+y+30 = 0

d%22%22=%22%22abs%28%284%2A%28-4%29%2B1%283%29%2B30%29%2Fsqrt%28%284%29%5E2%2B%281%29%5E2%29%29

d%22%22=%22%22abs%28%28-16%2B3%2B30%29%2Fsqrt%2816%2B1%29%29

d%22%22=%22%2217%2Fsqrt%2817%29%22%22=%22%22expr%2817%2Fsqrt%2817%29%29%2Aexpr%28sqrt%2817%29%2Fsqrt%2817%29%29%22%22=%22%2217sqrt%2817%29%2F17%22%22=%22%22sqrt%2817%29

So the radius r = sqrt%2817%29

And the radius squared is r2 = 17 , and the center is
(h,k) = (-4,3), so the equation of that circle is

(x-h)2+(y-k)2 = r2

or

(x+4)2+(y-3)2 = 17

Edwin

Answer by ikleyn(52770) About Me  (Show Source):
You can put this solution on YOUR website!
.
If you are unfamiliar with the formula for the distance from the point to the straight line
in a coordinate plane or want to know more about it,  you can read about it in the lesson

      HOW TO calculate the distance from a point to a straight line in a coordinate plane

in this site.

It is prepared specially for you!