SOLUTION: Which of these is the equation for a line tangent to the circle x^2 + y^2 = 20 at point (2, -4)? y = ½x + √20 y = 2x – 5 y = 2x + √20 y = ½x – 5

Algebra ->  Equations -> SOLUTION: Which of these is the equation for a line tangent to the circle x^2 + y^2 = 20 at point (2, -4)? y = ½x + √20 y = 2x – 5 y = 2x + √20 y = ½x – 5       Log On


   

Question 1080222: Which of these is the equation for a line tangent to the circle x^2 + y^2 = 20 at point (2, -4)?

y = ½x + √20
y = 2x – 5
y = 2x + √20
y = ½x – 5
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
To find the slope, calculate the derivative at the point.
Using implicit differentiation,
2xdx%2B2ydy=0
ydy=-xdx
dy%2Fdx=-x%2Fy
So at (2,-4),
m=dy%2Fdx=-2%2F-4=1%2F2
Using the point-slope form of a line,
y-%28-4%29=%281%2F2%29%28x-2%29
y%2B4=x%2F2-1
y=x%2F2-5
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