An ellipse has equationx2+ 2xy+ 4y2= 16(a) Calculate a formula fordydx, the derivative ofywith respect tox.(b) Find an equation for the line which is tangent to ellipse at the point (4,−2).(c) Find the locations where the ellipse has horizontal tangent lines (dydx= 0 ) 1. An ellipse has equation x2 + 2xy + 4y2 = 16(a) Calculate a formula for d, the derivative of y with respect to x.(b) Find an equation for the line which is tangent to ellipse at the point (4,-2).(c) Find the locations where the ellipse has horizontal tangent lines ( = 0)dx

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1. An ellipse has equation x?+ 2xy+ 4y2 = 16 (a) Calculate a formula for dy the derivative of y with respect to x. (b) Find an equation for the line which is tangent to ellipse at the point (4, -2)- (c) Find the locations where the ellipse has horizontal tangent lines ( = 0 )

1. An ellipse has equation x?+ 2xy+ 4y2 = 16 (a) Calculate a formula for dy the derivative of y with respect to x. (b) Find an equation for the line which is tangent to ellipse at the point (4, -2)- (c) Find the locations where the ellipse has horizontal tangent lines ( = 0 )

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter8: Polar Coordinates And Parametric Equations

Section8.CT: Chapter Test

Problem 8CT

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

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An ellipse has equationx2+ 2xy+ 4y2= 16(a) Calculate a formula fordydx, the derivative ofywith respect tox.(b) Find an equation for the line which is tangent to ellipse at the point (4,−2).(c) Find the locations where the ellipse has horizontal tangent lines (dydx= 0 )

1. An ellipse has equation x2 + 2xy + 4y2 = 16
(a) Calculate a formula for d, the derivative of y with respect to x.
(b) Find an equation for the line which is tangent to ellipse at the point (4,-2).
(c) Find the locations where the ellipse has horizontal tangent lines ( = 0)
dx

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