A curve having the condition that the slope of the tangent at some point is two times the slope of the straight lines joining the same point to the origin of co-ordination is a/an
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a
circle
b
ellipse
c
parabola
d
hyperbola
answer is C.
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Detailed Solution
Let p(x,y) be any point on the curve, then dydx=2yx→∫dyy=2∫dxx⇒logy=logcx2→y=cx2 is a parabola.
A curve having the condition that the slope of the tangent at some point is two times the slope of the straight lines joining the same point to the origin of co-ordination is a/an