Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-1>Q 74

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The equation of tangent drawn to the curve $x y = 4$ from point $(0, 1)$ is

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Important Questions on Application of Derivatives

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-1>Q 75

The curve

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

has a vertical tangent at :

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-1>Q 76

If the tangent to the curve

x = a (θ + \sin θ), y = a (1 + \cos θ)

at

θ = \frac{π}{3}

makes an angle

α (0 \leq α < π)

with

x

-axis, then

α =

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-1>Q 77

If the normal at the point

(3 t, \frac{4}{t})

of the curve

x y = 12

cuts the curve again at

(3 t_{1}, \frac{4}{t_{1}})

then find

t_{1}

in terms of

' t'

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-1>Q 78

The common tangent of the curves $y = x^{2} + \frac{1}{x}$ and $y^{2} = 4 x$

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-1>Q 80

The angle of intersection of

y = a^{x}

and

y = b^{x}

, is given by:

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-1>Q 81

The angle between the curves

x^{2} + 4 y^{2} = 32

and

x^{2} - y^{2} = 12

, is:

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-1>Q 82

Find the angle at which two curves

x^{3} - 3 x y^{2} + 2 = 0

and

3 x^{2} y - y^{3} - 2 = 0

intersect

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Alpha Question Bank for Engineering: Mathematics>Chapter 28 - Application of Derivatives>Exercise-1>Q 84

The shortest distance between curves

y^{2} = 8 x

and

y^{2} = 4 (x - 3)

is