How do you find the equations for the normal line to x^2+y^2=20 through (2,4)?

2 Answers
Apr 23, 2017

y=2x

Explanation:

y-0 = (4-0)/(2-0)(x-0)

y=2x

:)))

Apr 23, 2017

The equation is y =2x.

Explanation:

The derivative of this relation is given by

2x + 2y(dy/dx) = 0

2y(dy/dx) = -2x

dy/dx= -x/y

The slope of the tangent line is

m_"tangent" = -2/4 = -1/2

Therefore, the slope of the normal line is 2.

y - 4 = 2(x - 2)

y- 4= 2x - 4

y = 2x, as obtained in the other answer

Hopefully this helps!