Posted by Shayne on Wednesday, September 14, 2011 at 9:35pm.
Find an equation of the normal line to the parabola
y = x2 − 7x + 5
that is parallel to the line
x − 3y = 3.
- calculus - Reiny, Wednesday, September 14, 2011 at 10:29pm
dy/dx = 2x-7 which is the slope of the tangent.
so the normal must have a slope of -1/(2x-7) or 1/(7-2x)
but that is supposed to be parallel to x-3y=3
that is, a slope of 1/3
1/(7-2x) = 1/3
3 = 7-2x
2x = 4
x = 2
when x=2, y = 4-14+5 = -5
so the normal has equation
x - 3y = c
with (2,-5) on it, so
2 + 15 = c
equation of normal is
x - 3y = 15
check: at (2,-5) slope should be -3
dy/dx = 2(2)-7 = -3
My answer for the equation of the normal is correct!!
Answer This Question
More Related Questions
- Calculus - Find an equation of the normal line to the parabola y=x^2−8x+1 ...
- calculus - Find parametric equations for the line through the point P(2, 9, 4) ...
- vectors linear algebra - The parametric equations for a line L1 are as follows: ...
- calculus: multivariable - Find the points on the hyperboloid x2 −y2 +2z2...
- Mathamatics - This question concerns the straight line that passes through the ...
- Math - This question concerns the straight line that passes through the points...
- algebra - Which choice is the equation of a line that passes through the point (...
- Calc. - I am so confused with this last part of the unit! What in the world is ...
- Math - The parametric equations for a line L1 are as follows: x = 2+2t y = 2+2t ...
- linear algebra - Let L be the line with parametric equations x = −5+2t y...