Question

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

Answer 1

(see attached workings)

y = -4x + 2

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

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.