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Use Implicit Differentiation to find equation of tangent line to ellipse 5x^2+xy+4y^2=40 at the point (−2,−2)

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Use implicit differentiation to find an equation of the tangent line to the ellipse defined by  5x^2+xy+4y^2=40 at the point (−2,−2)

asked Oct 27, 2017 in CALCULUS by 1ndig0 Rookie

1 Answer

+1 vote

5x2+xy+4y2=40

Take derivative both sides.

(d/dx)(5x2+xy+4y2)=0

10x+x(dy/dx)+y+8y(dy/dx)=0

(dy/dx)(x+8y)+10x+y=0

dy/dx=-(10x+y)/(x+8y)

dy/dx(-2,-2) =-((10*-2)+(-2))/((-2)+8(-2))

               =+22/-18

               =-11/9

Calculate the tangent equation.

(y-(-2))=-( 11/9)(x-(-2))

y+2=-(11/9)(x+2)

9y+18=-11x-22

11x+9y+40=0

answered Oct 28, 2017 by lilly Expert

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