Question

At what points on the curve x2 + y2 – 2x – 4y + 1 = 0 is the tangent parallel to x-axis.

Answer 1

Given Curve is x2 + y2 – 2x – 4y + 1 = 0 …(i)

Differentiating (i) w.r.t. x, we have

=> y – 2 = 0

=> y = 2

Put y = 2 in (i), we get

x2 + 4 – 2x – 8 + 1 = 0

=> x2 – 2x – 3 = 0

=> x = 3, –1

Hence, At (3,2) and (–1,2) the tagents to curve (i) are parallel to y-axis.