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Question

A curve having the condition that the slope of the tangent at some point is two times the slope of the straight line joining the same point to the origin of coordinates is a/an


A

circle

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B

ellipse

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C

parabola

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D

hyperbola

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Solution

The correct option is C

parabola


Explanation for the correct option:

Step 1: Find the slope of the straight line joining the point to the origin of coordinates.

Let P(x,y)be any point on the curve.

the slope of the straight line joining the point P(x,y) to the origin of coordinates would be,

m=y-0x-0

Step 2: Formulate the given problem into mathematical expressions.

dydx=2mdydx=2yx

Step 3: Find the equation of the curve.

dydx=2yx1ydy=21xdx1ydy=21xdxlogy=2logx+logCy=Cx2

This curve represents a parabola.

Therefore, option (C) is the correct answer.


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