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. $y(x-a)=a^2$
• B. $y(x+a)=a^2$
• C. $x(y-a)=a^2$
• D. $x(y+a)=a^2$

Answer 1

Answer: (A)

We have,
Cartesian subtangent + abscissa = constant
$\Rightarrow \frac{y}{dy/dx}+x=a$
$\Rightarrow y\frac{dx}{dy}+x=a$
$\Rightarrow \frac{dy}{y}=\frac{dx}{a-x}$
Integrating, we get
$\log y+\log (x-a)=\log c$
$\therefore y(x-a)=c$
As the curve passes through the point $(2a,a)$, we have $c=a^2$
Hence, the required curve is $y(x-a)=a^2$.