Consider the closed curve in the xy - plane given by: x² + 2x + y* + 4y = 5. -(z+1) 2(y8+1) dy a) Show that dr b) Write an equation for the line tangent to the curve at the point (2, -1). c) Find the coordinates of the two points on the curve where the line tangent to the curve is vertical.

Trigonometry (MindTap Course List)
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ISBN:9781337278461
Author:Ron Larson
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Chapter6: Topics In Analytic Geometry
Section6.6: Parametric Equations
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Consider the closed curve in the xy - plane given by: x² + 2x + y* + 4y = 5.
-(z+1)
2(y3+1)
dy
a) Show that
dr
b) Write an equation for the line tangent to the curve at the point (2, -1).
c) Find the coordinates of the two points on the curve where the line tangent to the curve is vertical.
d) Is it possible for this curve to have a horizontal tangent at points where it intersects the x-axis? Explain your reasoning.
Transcribed Image Text:Consider the closed curve in the xy - plane given by: x² + 2x + y* + 4y = 5. -(z+1) 2(y3+1) dy a) Show that dr b) Write an equation for the line tangent to the curve at the point (2, -1). c) Find the coordinates of the two points on the curve where the line tangent to the curve is vertical. d) Is it possible for this curve to have a horizontal tangent at points where it intersects the x-axis? Explain your reasoning.
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