Q. A curve having the condition that the slope of tangent at some point is two times the slope of the straight line joining the same point to the origin of coordinates, is a/an
A) Circle
B) Ellipse
C) Parabola
D) Hyperbola
Explanation
(c)
Given, $\frac{dy}{dx} = 2\ \frac{y}{x}$ $(\therefore y = mx)$
$\Rightarrow$ $\int_{}^{}\frac{dy}{y} = 2\int_{}^{}\frac{dx}{x}$
$\Rightarrow$ $\log y = 2\log x + \log c$
$\Rightarrow$ $y = cx^{2}$
Which represent a parabola of the form
$x^{2} = 4ay$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.