Question

The distance between the origin and the normal to the curve

y = e^2x + x² drawn at the point x = 0 is –

• A. 1/√5
• B. 2/√5
• C. –1/√5
• D. 2/√3

Answer 1

Answer: (B)

2/√5

Answer 2

The equation of the curve is y = e^2x + x², when x = 0,

y = 1

$\frac{dy}{dx}$ = 2e^2x + 2x = 2 at the point (0, 1)

∴ slope of the normal = (1/2) and the normal passes through the point (0, 1)

∴ the normal has the equation y – 1 = – (1/2)x

⇒ x + 2y – 2 = 0, ∴ required distance = 2/√5