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

The correct option is A $y(x-a)=a^2$

We have Cartesian sub tangent+abscissa = constant
$\Rightarrow \frac{y}{\left(\frac{dy}{dx}\right)}+x=a\Rightarrow y\frac{dx}{dy}+x=a\Rightarrow \frac{dy}{y}=\frac{dx}{a-x}$
Integrating we get $logy+log(x-a)=logc\therefore y(x-a)=c$
As the curve passes through the point (2a, a) we have
$c=a^2$
$\therefore$ the required curve is $y(x-a)=a^2$