GATE CSE 1995 | Question: 1.22

Question

If at every point of a certain curve, the slope of the tangent equals $\frac{-2x}{y}$ the curve is

• A. a straight line

• B. a parabola

• C. a circle

• D. an ellipse

Answer 1

The slope of the tangent  −2x/y

that is  dy/dx = -2x/y    
         ydy   = -2xdx
         
itegrating both the side
          
          y^2/2  = -2*x^2/2 + c
          
          y^2/2 + x^2 = c
          
          it is in the form of x^2 / a^2 + y^2 / b^2 =c
          
          so the curve is an ellipse with a =1 and b = √2.

Answer 2

ans is D

an ellipse

Comments

Can u please explain a bit