SOLUTION: (a) find an equation for the line tangent to the circle x^2+ y^2=25 at the point (3,-4). (b) At what other point on the circle will a tangent line be parallel to the tangent line

Algebra ->  Graphs -> SOLUTION: (a) find an equation for the line tangent to the circle x^2+ y^2=25 at the point (3,-4). (b) At what other point on the circle will a tangent line be parallel to the tangent line       Log On


   

Question 1070322: (a) find an equation for the line tangent to the circle x^2+ y^2=25 at the point (3,-4).
(b) At what other point on the circle will a tangent line be parallel to the tangent line in part (a)?
Found 2 solutions by josgarithmetic, Alan3354:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The point (3,-4) is in quadrant 4, for the lower half of the circle.
y=-%2825-x%5E2%29%5E%281%2F2%29

dy%2Fdx=x%2Fsqrt%2825-x%5E2%29, skipping the steps here.
At x=3, dy%2Fdx=3%2F4, the slope for the line on the circle at point (3,-4).
That tangent line: highlight%28y%2B4=%283%2F4%29%28x-3%29%29.

(b)
Can you do this part?

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
(a) find an equation for the line tangent to the circle x^2+ y^2=25 at the point (3,-4).
The slope of the tangent line at any point on a circle is -x/y
--> m = 3/4
y + 4 = (3/4)*(x - 3)
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(b) At what other point on the circle will a tangent line be parallel to the tangent line in part (a)?
At the other end of the diameter (-3,4)