if -xy+ 1 + x^2 = 2y then find the equations of all tangent lines to the curve y= -2

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01-02-2022
Mathematics

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if -xy+ 1 + x^2 = 2y then find the equations of all tangent lines to the curve y= -2

Sagot :

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semsee45 semsee45 · Answer 1 · 2022-02-01T08:51:24-05:00

semsee45 semsee45

01-02-2022

Answer:

(see attached workings)

y = -4x + 2

y = (4/5)x + 2/5

Step-by-step explanation:

Rewrite the function to make y the subject.
Find the x values of the points when y=-2 by substituting y=-2 into the rewritten function
Differentiate the function
Input the found values of x into the differentiated function to find the gradients of the tangents to the curve at y=-2
Use the equation of a straight line and the points where y=-2 and the found gradients to find the equation of the tangent lines.

See attached for complete step-by-step.

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