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B. x² + 3xy-5y² = 5 at (2, 1) C. xy² + y = 14 at (3,2)

B. x² + 3xy-5y² = 5 at (2, 1) C. xy² + y = 14 at (3,2)

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section6.2: Introduction To Conics: parabolas
Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.
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Need help with problem 1 part B and C
1. Find an equation for the tangent line to the graph of the given equation at the specified point. You will need to implicit differentiation. A. x² + y² = 25 at (4, -3) B. x² + 3xy-5y² = 5 at (2, 1) C. xy + y = 14 at (3, 2) 2. Consider a circle that is expanding in size with time t in seconds. Use the area of a circle equation A = ² for t problem. A. You are told that the radius is increasing at a rate of 3 cm/s. Find the rate of change of the area A (measured i cm^2) with respect to time t (measured in s) at the moment when r = 3 cm. B. You are now instead told that the area is increasing at a rate of 3 cm^2/s. Find the rate of change of the radius (measured in cm) with respect to time t (measured in s) at the moment when r = 3 cm. 3. A 13 ft ladder is sliding down a wall as depicted below. Use the Pythagorean Theorem x² + y² = 13² for this problem. y ladder 13 St A. You are told that at this very moment the bottom of the ladder is 5 ft from the wall and is sliding away from the wall at 2 ft/min. Find the rate at which the top of the ladder is sliding down the wall.
Transcribed Image Text:1. Find an equation for the tangent line to the graph of the given equation at the specified point. You will need to implicit differentiation. A. x² + y² = 25 at (4, -3) B. x² + 3xy-5y² = 5 at (2, 1) C. xy + y = 14 at (3, 2) 2. Consider a circle that is expanding in size with time t in seconds. Use the area of a circle equation A = ² for t problem. A. You are told that the radius is increasing at a rate of 3 cm/s. Find the rate of change of the area A (measured i cm^2) with respect to time t (measured in s) at the moment when r = 3 cm. B. You are now instead told that the area is increasing at a rate of 3 cm^2/s. Find the rate of change of the radius (measured in cm) with respect to time t (measured in s) at the moment when r = 3 cm. 3. A 13 ft ladder is sliding down a wall as depicted below. Use the Pythagorean Theorem x² + y² = 13² for this problem. y ladder 13 St A. You are told that at this very moment the bottom of the ladder is 5 ft from the wall and is sliding away from the wall at 2 ft/min. Find the rate at which the top of the ladder is sliding down the wall.
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