SOLUTION: find the equation of the tangents to the circle x2 +y2=9 with slope 1

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Question 1040185: find the equation of the tangents to the circle x2 +y2=9 with slope 1
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Find the derivative.
2xdx%2B2ydy=0
2ydy=-2xdx
dy%2Fdx=-x%2Fy
So when y=-x, the derivative (which is the slope of the tangent line) is equal to 1.
To find the points, plug this into the original equation.
x%5E2%2B%28-x%29%5E2=9
2x%5E2=9
x%5E2=9%2F2
x=0+%2B-+3%2Fsqrt%282%29
x=0+%2B-+%283%2F2%29sqrt%282%29
Then using the point-slope form,
y-%283%2F2%29sqrt%282%29=1%28x%2B%283%2F2%29sqrt%282%29%29
y=x%2B3sqrt%282%29
and
y%2B%283%2F2%29sqrt%282%29=1%28x-%283%2F2%29sqrt%282%29%29
y=x-3sqrt%282%29
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