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

Question 1040552: Center at (-4,3), tangent to the line y= -4x-30
Found 3 solutions by josgarithmetic, Edwin McCravy, ikleyn:
Answer by josgarithmetic(39617)   (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 passing through the given center (-4,3). This is

A point ON the circle is the intersection of .

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)   (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: The line y= -4x-30 is the line 4x+y+30 = 0 So the radius r = 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(52777)   (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!

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