Question

A ray of light coming from origin after reflection at the point P (x, y) of any curve becomes parallel to x-axis, the equation of the curve may be –

• A. y² = x
• B. y² = 2x + 1
• C. y² = 4x
• D. y² = 4x + 1

Answer 1

Answer: (B)

y² = 2x + 1

Answer 2

The slope of the ray = $\frac{y}{x}$

Slope of the normal at P (x, y) = – $\frac{dx}{dy}$

Ž $\frac{\frac{y}{x} + \frac{dx}{dy}}{1 - \frac{y}{x}\frac{dx}{dy}}$

Ž$\frac{dx}{dy}$ + 1 = – 1 + $\frac{dx}{dy}$ Ž y $\left( \frac{dy}{dx} \right)^{2}$ + 2x$\frac{dy}{dx}$ = y is differential equation of the curve which is satisfied by

y² = 2x +1.

Hence (2) is the correct answer