490 views

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 | 490 views

+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)