SOLUTION: given circle (x+3)^2+(y+2)^2=20 with tangent KL touching the circle at K.Determine 1 the length of KL,if point L=(7;-2) 2 the coordinates of point K,the point of contact of the t

Question 1088731: given circle (x+3)^2+(y+2)^2=20 with tangent KL touching the circle at K.Determine
1 the length of KL,if point L=(7;-2)
2 the coordinates of point K,the point of contact of the tangent to the circle
3 the equations of the tangents KL
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
KCL forms a right triangle (C is the center of the circle).
You know the hypotenuse (CL), you know the length of KC.
Solve for KL.

So build a circle centered at (7,-2) with a radius squared of 80.

Find the intersection of the two circles, that'll be point K.
From the first circle,

Substitute into the second circle,

Then,

or
Now that you know K (-1,2) and L (7,-2) you can get the line that goes through both.
Slope:
Using the point slope form,

.
.
.

.
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