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JEE MATHEMATICS MCQ: TANGENTS & NORMALS

1 Easy

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Application +4 | -1

The tangents to the curve

x = a\left( {\theta - \sin \theta } \right),\;y = a\left( {1 + \cos \theta } \right)

at the points

\theta = \left( {2k + 1} \right)\pi ,\;k \in Z

are parallel to:

View answer and explanation

Correct option: C

y = 0

Option C (

y = 0

) is correct because the slope

\frac{{dy}}{{dx}}

is 0 at

\theta = (2k+1)\pi

, indicating a horizontal tangent.

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The complete set of value of '

a

' for which there exists at least one line that is tangent to the graph of the curve

y=x^3-a x

at one point and normal to the graph at another point is given by The point of intersection of the tangents drawn to the curve

x^2 y=1-y

at the points where it is met by the curve

x y=1-y

, is given by Let

C

y^3-3 x y+2=0

H

is the set of points on the curve

\mathrm{C}

where the tangent is parallel to

x

V

is the set of points on

C

where the tangent is parallel to

y

-axis, then The curve

y-e^{x y}+x=0

has a vertical tangent at the point: If normal to the curve

y = f\left( x \right)

x

-axis, then The angle of intersection between the curves

{x^2} = 4\left( {y + 1} \right)

{x^2} = - 4\left( {y + 1} \right)