HSC Arts Class 12 - Tamil Nadu Board of Secondary Education Question Bank Solutions

Find the points on the curve y² – 4xy = x² + 5 for which the tangent is horizontal

Find the tangent and normal to the following curves at the given points on the curve

y = x² – x⁴ at (1, 0)

Find the tangent and normal to the following curves at the given points on the curve

y = x⁴ + 2e^x at (0, 2)

Find the tangent and normal to the following curves at the given points on the curve

y = x sin x at `(pi/2, pi/2)`

Find the tangent and normal to the following curves at the given points on the curve

x = cos t, y = 2 sin²t at t = `pi/2`

Find the equations of the tangents to the curve y = 1 + x³ for which the tangent is orthogonal with the line x + 12y = 12

Find the equations of the tangents to the curve y = `- (x + 1)/(x - 1)` which are parallel to the line x + 2y = 6

Find the equation of tangent and normal to the curve given by x – 7 cos t andy = 2 sin t, t ∈ R at any point on the curve

Find the angle between the rectangular hyperbola xy = 2 and the parabola x² + 4y = 0

Show that the two curves x² – y² = r² and xy = c² where c, r are constants, cut orthogonally

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The volume of a sphere is increasing in volume at the rate of 3π cm³/ sec. The rate of change of its radius when radius is `1/2` cm

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A balloon rises straight up at 10 m/s. An observer is 40 m away from the spot where the balloon left the ground. The rate of change of the balloon’s angle of elevation in radian per second when the balloon is 30 metres above the ground

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The position of a particle moving along a horizontal line of any time t is given by s(t) = 3t² – 2t – 8. The time at which the particle is at rest is

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A stone is thrown, up vertically. The height reaches at time t seconds is given by x = 80t – 16t². The stone reaches the maximum! height in time t seconds is given by

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Find the point on the curve 6y = x³ + 2 at which y-coordinate changes 8 times as fast as x-coordinate is

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The abscissa of the point on the curve f(x) = `sqrt(8 - 2x)` at which the slope of the tangent is – 0.25?

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The slope of the line normal to the curve f(x) = 2 cos 4x at x = `pi/12` is

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The tangent to the curve y² – xy + 9 = 0 is vertical when

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Angle between y² = x and x² = y at the origin is

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The maximum slope of the tangent to the curve y = e^x sin x, x ∈ [0, 2π] is at