How do you find the equations for the

Raven Gardner

Raven Gardner

Answered question

2022-04-18

How do you find the equations for the normal line to x2y2=16 through (5,3)?

Answer & Explanation

Sabrina Campos

Sabrina Campos

Beginner2022-04-19Added 13 answers

Explanation:
Equation of normal at x=x0 on the curve y=f(x) is perpendicular to the tangent at x=x0 at f(x).
As slope of tangent at x=x0 on the curve f(x), is given by f(x0), slope of normal is 1f(x0) and equation of normal is
y=1f(x0)(xx0)+f(x0)
As x2y2=16 taking derivative w.r.t. x, we get
2x2ydydx=0 of f(x)=dydx=xy
Hence slope of tangent at (5,3) is 53 and slope of normal is 35.
Hence equation of normal is y3=35(x5) or 3x+5y-30=0

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