Question

The eccentricities of the curves for which the length of the normal is equal to the length of the radius of the vector is/are ______

• A. $0,\sqrt{2}$
• B. $1,\sqrt{2}$
• C. $\frac{3}{2},0$
• D. $\frac{3}{2},\sqrt{2}$

Answer 1

The correct option is A $0,\sqrt{2}$

$x_1^2+y_1^2=(m^2+1)y_1^2⟹\frac{dy}{dx}=\pm \frac{y}{x}⟹xy=c;y=x+c⟹\sqrt{2},0$ are eccentricities.