Engineering Board Exam Reviewer · Tangent and Normal Lines · medium

Find the equation of the normal line to y= x at x=4.

1. x-4y=-4
2. 4x-y=14
3. x+4y=12
4. 4x+y=18

Answer

D. 4x+y=18

Solution

At x=4, y=2 and y'=1/2 x= 14. The normal slope is -4: y-2=-4(x-4) 4x+y=18. (The tangent would be x-4y=-4.)

More Tangent and Normal Lines questions

1. Find the equation of the tangent line to y=x2 at the point (3,9).
2. Find the slope of the tangent line to y=x3-2x at x=2.
3. Find the area of the triangle formed by the coordinate axes and the tangent line to y= 1x at x=2.
4. Find the equation of the tangent line to x2+xy+y2=7 at the point (2,1).
5. Find the points on y=x3-3x+1 where the tangent line is horizontal.
6. Find the angle of inclination (in degrees) of the tangent line to y=x2 at x=1.
7. At what point on the curve y=x2-4x+5 is the tangent line parallel to the line y=2x+1?

All Tangent and Normal Lines questions