JEE MATHEMATICS MCQ: TANGENTS & NORMALS

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Analyzing +4 | -1

The tangent and normal at the point

P\left( {a{t^2},\;2\;at} \right)

to the parabola

{y^2} = 4\;ax

meet the

x

-axis in

T

and

G

respectively, then the angle at which the tangent at

P

to the parabola is inclined to the tangent at P to the circle through

T,\;P,\;G

View answer and explanation

Correct option: C

{\tan ^{ - 1}}t

Option C (

{\tan ^{ - 1}}t

) is correct because the angle between the tangents is found using the slopes of the tangent to the parabola and the tangent to the circle at point P.

More Questions from TANGENTS & NORMALS

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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

be the curve

y^3-3 x y+2=0

. If

H

is the set of points on the curve

\mathrm{C}

where the tangent is parallel to

x

-axis and

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)

is parallel to

x

-axis, then 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: