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Question 1120517: For what values of m is the line y=mx, a tangent to the parabola y= x^2 - 8x + 25? Thank you :)
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! y = f(x) = x^2 -8x +25
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let (a,f(a)) be a point on f(x)
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the tangent line at (a,f(a)) is
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y = f'(a)(x-a)+f(a)
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f'(x) = 2x -8, f(a) = a^2 -8a +25
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f'(a) = 2a -8
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y = 2a -8(x-a) +a^2 -8a +25
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y = -a^2 +2ax -8x +25
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we want y = mx, then
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-a^2 +25 = 0
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a^2 = 25
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a = 5 or -5
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m = f'(a) = 2a -8
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m = 2 or -18
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