find the points at which the graph of the equation

Question

4x^2 + y^2 -8x +4y +4=0 has a vertical or horizontal tangent line

Answer 1

The curve equation is

Recall that slope of the horizontal line is zero and slope of the vertical line is undefined.

The curve has horizontal tangent lines.

Tangent line slope is y'.

Differentiate implicitly.

Equate the y' = 0.

Substitute x = 1 in the curve and solve for y.

Tangent points are (1, 0) and (1, - 4).