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. $y(y-a)=a^2$
• D. $y(y+a)=a^2$

Answer 1

Answer: (A)

$y(x-a)=a^2$

We have, cartesian subtangent+abscissa=constant
$\Rightarrow \frac{y}{\frac{dy}{dx}}+x=a\Rightarrow y\frac{dy}{dx}+x=a\Rightarrow \frac{dy}{y}=\frac{dx}{a-x}$
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 $y(x-a)=a^2.$