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

  1. a straight line

  2. a parabola

  3. a circle

  4. an ellipse

in Non GATE by Veteran (52.3k points) | 490 views

3 Answers

+1 vote
ans is D

an ellipse
by Loyal (8.1k points)
0
Can u please explain a bit
+1 vote
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.
by (355 points)
–1 vote
a) st.line
by Loyal (5.2k points)

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