Question

The equation of the curve which passes through the point

(2a, a) and for which the sum of the Cartesian sub tangent and the abscissa is equal to the constant a, is –

• A. y (x – a) = a²
• B. y (x + a) = a²
• C. x (y – a) = a²
• D. x (y + a) = a²

Answer 1

Answer: (A)

y (x – a) = a²

Answer 2

We have,

Cartesian sub tangent + abscissa = constant

⇒ $\frac{y}{dy/dx}$ + x = a ⇒ y $\frac{dx}{dy}$ + x = a

⇒ $\frac{dy}{y}$= $\frac{dx}{a - x}$

Integrating , we get

log y + log (x – a) = log c

∴ y (x – a) = c.

As the curve passes through the point (2a, a), we have

c = a²

∴ The required curve is y (x – a) = a²

Hence (1) is the correct answer.