JEE MATHEMATICS MCQ: TANGENTS & NORMALS

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Application +4 | -1

If the two curves

y=a^x

and

y=b^x

intersect at an angle

\alpha

, then tan

\alpha

equals -

View answer and explanation

Correct option: A

\frac{\log b-\log a}{1+\log a \log b}

Option A (

\frac{{\log b - \log a}}{{1 + \log a \log b}}

) is correct because the tangent of the angle between the two curves is found by calculating the derivatives of the curves at their point of intersection and then using the formula for the tangent of the angle between two lines.

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: