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Find the smallest distance between the graphs of y = x^2 - 4x + 12 and y = 2x + 1.
- Joined
- Apr 12, 2005
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- 11,339
Match the derivative.
2x - 4 = 2 ==> x = 3
Point on Parabola
3^2 -4*3 + 12 = 9 - 12 + 12 = 9 ==> (3,9)
Distance from Point to Line
Line: 2x - y + 1 = 0
Point: (3,9)
\(\displaystyle \L\,\frac{|2*3 - 1*9 + 1|}{\sqrt{2^{2}+1^{2}}} = \frac{2}{5}\sqrt{5}\)
Simple enough ideas. Are they not covered in your book or your class?
2x - 4 = 2 ==> x = 3
Point on Parabola
3^2 -4*3 + 12 = 9 - 12 + 12 = 9 ==> (3,9)
Distance from Point to Line
Line: 2x - y + 1 = 0
Point: (3,9)
\(\displaystyle \L\,\frac{|2*3 - 1*9 + 1|}{\sqrt{2^{2}+1^{2}}} = \frac{2}{5}\sqrt{5}\)
Simple enough ideas. Are they not covered in your book or your class?