Question

The equation of tangent to the curve y (1 + x²) = 2 – x, where it crosses x-axis is:

A. x + 5y = 2
B. x – 5y = 2
C. 5x – y = 2
D. 5x + y = 2

Answer 1

Given the equation of the curve is

y (1 + x²) = 2 – x

Differentiating on both sides with respect to x, we get

We know derivative of a constant is 0, so above equation becomes

As the given curve passes through the x-axis, i.e., y=0,

So the equation on given curve becomes,

y(1+x²)=2-x

⇒ 0(1+x²)=2-x

⇒ 0=2-x

⇒ x=2

So the given curve passes through the point (2,0)

So the equation (i) at point (2,0) is,

Hence, the slope of tangent to the curve is -1/5

Therefore, the equation of tangent of the curve passing through (2,0) is given by

⇒ 5y=-x+2

⇒ x+5y=2

So the equation of tangent to the curve y (1 + x²) = 2 – x, where it crosses x-axis is x+5y=2.

Therefore the correct option is option A.