Question

Tangent to a curve intersect the y axis at a point P. A line perpendicular to this tangent through P passes through point (1, 0). The differential equation of the curves is

• A. y. $\frac{dy}{dx} - x\left( \frac{dy}{dx} \right)^{2}$= 0
• B. x$\frac{d^{2}y}{dx^{2}} + \left( \frac{dy}{dx} \right)^{2}$= 1
• C. y. $\frac{dx}{dy}$ + x = 1
• D. None of these

Answer 1

Answer: (A)

y. $\frac{dy}{dx} - x\left( \frac{dy}{dx} \right)^{2}$= 0

Answer 2

Equation of tangent at the point

R (x, f(x)) is Y – f(x) = f '(x) (X – x)

Coordinate of point P is (0, f(x) – x f '(x))

The slope of the perpendicular line through 'P' is

$\frac{f(x) - xf'(x)}{- 1} = - \frac{1}{f'(x)}$

y$\frac{dy}{dx}$ – x $\left( \frac{dy}{dx} \right)^{2}$ = 1 is differential equation