The best way to Find an equation of the normal line to the parabola is to eliminate as many options as possible.
Find an equation of the normal line to the parabola y = x 2 − 9x + 5 that is parallel to the line x − 5y = 1
We have a parabola with the equation: y = x2 − 8x +9. Differentiating wrt x we have: dy dx = 2x − 8. If we consider the line: x − 2y = 3. and putting into the standard form, y = mx +c, we have: 2y = x − 3 ⇒ y = 1 2 x − 3 2.
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The answer to the equation is 4.
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