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  • 04-08-2020
  • Mathematics
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Consider the circle of radius 10 centered at the origin. Find an equation of the line tangent to the circle at the point (6, 8)

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MathPhys
MathPhys MathPhys
  • 04-08-2020

Answer:

y = -3/4 x + 25/2

Step-by-step explanation:

x² + y² = 100

Take derivative with respect to x.

2x + 2y dy/dx = 0

2y dy/dx = -2x

dy/dx = -x/y

Evaluate at (6, 8).

dy/dx = -6/8

dy/dx = -3/4

Use point-slope form to write equation:

y − 8 = -3/4 (x − 6)

Simplify.

y − 8 = -3/4 x + 9/2

y = -3/4 x + 25/2

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