SOLUTION: How many lines with a slope of -1 are tangent to the circle x^2 + y^2 = 25

Question 437159: How many lines with a slope of -1 are tangent to the circle x^2 + y^2 = 25
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
How many lines with a slope of -1 are tangent to the circle x^2 + y^2 = 25
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x^2 + y^2 = 25
There would be two points where a line of -1 slope would be tangent to the circle. The (x,y) coordinates at the two points would be (5sqrt(2)/2,5sqrt(2)/2) and (-5sqrt(2)/2,-5sqrt(2)/2)
Using the standard form for a straight line, y=mx+b, we have (x,y) coordinates of a point on each line. All we need is find b to complete the equation.
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For the first line:
y=mx+b
5sqrt(2)/2=(-1)5sqrt(2)/2+b
5sqrt(2)=b
Equation of line: y=-x+5sqrt(2)
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For the second line:
y=mx+b
-5sqrt(2)/2=(-1)-5sqrt(2)/2+b
-5sqrt(2)=b
Equation of line: y=-x-5sqrt(2)
see graph below:
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y=+-(25-x^2)^.5
y=-x+5*2^.5
y=-x-5*2^.5

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