Use implicit differentiation to find an equation of the tangent line to the curve at the given point.

4x^2 + xy + 4y^2 = 9, (1, 1) (ellipse)

Question

Use implicit differentiation to find an equation of the tangent line to the curve at the given point.

4x^2 + xy + 4y^2 = 9,  (1, 1) (ellipse)

amistre64 · Answer

so, define the derivative for me

amistre64 · Answer

in other words, what is giving you an issue with this?

anonymous · Answer

I found  y=2-x so is that correct?

amistre64 · Answer

4x^2 + xy + 4y^2 = 9

8xx' + (xy)' + 8yy' = 0

8xx' + (x'y+xy') + 8yy' = 0

wrt.x this gives us  x'=dx/dx=1

8x + y+xy' + 8yy' = 0,  and solve for y'

y'(x+ 8y) = -y-8x

y' = (-y-8x)/(x+ 8y)

y' = -(y+8x)/(x+8y),  letting x=1, y=1 from the point

y' = -(1+8)/(1+8) = -1 for a slope

amistre64 · Answer

so point slope format is what ...

y = -(x-1)+1 ... so the tangent is y = -x+2

amistre64 · Answer

y=2-x is fine :)

anonymous · Answer

Thanks :)

amistre64 · Answer

youre welcome