Q17 of 292 Page 564

At what point on the curve , is the tangent parallel to the y-axis?

If the tangent is parallel to y-axis it means that it’s slope is

not defined or 1/0.

2y – 4 = 0 ⇒ y = 2

x² + (2)² – 2x – 4(2) + 1 = 0

⇒ x² – 2x – 3 = 0

⇒ x = 3 and x = -1

So, the requied points are (-1, 2) and (3, 2).

Show that the tangents to the curve at the point x = 2 and x = −2 are parallel.

Find the equation of the tangent to the curve , where is parallel to the line .

Find the point on the curve where the tangent is parallel to the x-axis.

Prove the tangent to the curve at the point (2, 0) and (3, 0) are at right angles.