Q19 of 149 Page 16

Find the point on the curve at which the tangents are parallel to y – axis

Since the tangent is parallel to y–axis, its slope is not defined, then the normal is parallel to x–axis whose The Slope is zero.

i.e., = 0

⇒ = 0

⇒ y = 0

Substituting y = 0 in = 1,

= 1

⇒ x² = 9

⇒ x = ±3

Thus, the required point is (3,0) & ( – 3,0)

Find the point on the curve x² + y² – 2x – 3 = 0 at which the tangents are parallel to the y – axis.

Find the point on the curve at which the tangents are parallel to x – axis

Show that the tangents to the curve y = 7x³ + 11 at the points x = 2 and x = – 2 are parallel.

Find the point on the curve y = x³ where the Slope of the tangent is equal to x – coordinate of the point.