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

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a

a circle

b

an ellipse

c

a parabola

d

a hyperbola

answer is C.

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Detailed Solution

Since, slope of line joining to point P(x, y) and origin is y/xSlope of tangent at P is dydxIt is given that,dydx=2yx⇒dyy=2dxx⇒∫dyy=2∫dxx⇒log⁡y=2log⁡x+log⁡C⇒y=x2Cwhich represents the equation of a parabola.
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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