How do you find the equations for the normal line to x^2+y^2=20x2+y2=20 through (2,4)?

2 Answers
Apr 23, 2017

y=2xy=2x

Explanation:

y-0 = (4-0)/(2-0)(x-0)y0=4020(x0)

y=2xy=2x

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Apr 23, 2017

The equation is y =2xy=2x.

Explanation:

The derivative of this relation is given by

2x + 2y(dy/dx) = 02x+2y(dydx)=0

2y(dy/dx) = -2x2y(dydx)=2x

dy/dx= -x/ydydx=xy

The slope of the tangent line is

m_"tangent" = -2/4 = -1/2mtangent=24=12

Therefore, the slope of the normal line is 22.

y - 4 = 2(x - 2)y4=2(x2)

y- 4= 2x - 4y4=2x4

y = 2xy=2x, as obtained in the other answer

Hopefully this helps!