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If: y = 5x +10 and y = x^2 +4

Then: x^2 +4 = 5x +10

Transposing terms: x^2 -5x -6 = 0

Factorizing the above: (x-6)(X+1) = 0 meaning x = 6 or x = -1

Therefore by substitution endpoints of the line are at: (6, 40) and (-1, 5)

Midpoint of line: (2.5, 22.5)

Slope of line: 5

Perpendicular slope: -1/5

Perpendicular bisector equation: y-22.5 = -1/5(x-2.25) => 5y = -x+114.75

Perpendicular bisector equation in its general form: x+5y-114.75 = 0

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It is x + 5y - 115 = 0

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Q: What is the perpendicular bisector equation of the line y equals 5x plus 10 spanning the parabola y equals x squared plus 4?
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What is the perpendicular bisector equation of the line y equals x plus 5 spanning the circle x2 plus 4x plus y2 -18y plus 59 equals 0?

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