Tangent and Normal

If the parametric equation of a curve is given by x = et cos t, y = et sin t, then the tangent to the curve at the point makes with the x-axis an angle of

For the parabola y² = 4ax, the ratio of the subtangent to the abscissa is

If y = 4x - 5 is a tangent to the curve y² = px³ + q at (2,3), then

The length of the normal to the curve y = a²(et/x + e-x/a) is

If the area of the triangle enclosed between the axes and any tangent to the curve xy = aⁿ is constant, then n is

The tangent lines drawn from the origin to the curve y = cos x have their points of contact lying on the curve

What is the value of the expression ∫(f'(x) f''(x) / f'(x)) dx from 0 to π/4?

What are the coordinates of the point R on the parabola y^2 = 2x, where the tangent to the curve is parallel to the chord PQ?

What is the equation of the normal to the curve y^2 = x^3 at the point whose abscissa is 8?

What is the number of tangents to the curve x^(3/2) + y^(3/2) = a^(3/2) that are equally inclined to the axes?

What are the coordinates of the points on the curve 9y^2 = x^3 where the normal to the curve cuts equal intercepts from the axes?

What is the change of the slope of the tangent to the curve at θ = 89.60 degrees?

What is the condition for the curves $y^2 = 2x^3$ and $4x - 3y + 2 = 0 to be perpendicular to each other at a point?

What is the equation of the normal to the parabola $y^2 = 4ax$ at a point $P$?

What is the length of the normal at any point on the catenary curve $y = c \/cosh\left(\frac{x}{c}\right)$?

What is the value of tanθ at the point P(2, 3) on the given curves?

What is the length of the tangent PA at point P(x, y) on the curve y = f(x)?

What is the condition for the tangent and normal to intersect at right angles at a point P on the curve?

What is the meaning of the subtangent and subnormal at a point P on the curve y = f(x)?

What is the significance of the point P in the context of tangents and normals?

If the area of the triangle enclosed between the axes and any tangent to the curve xy = aⁿ is constant, then n is

The tangent to the curve y² = px³ + q at (2, 3) is y = 4x - 5. Then, what are the values of p and q?

The length of the normal to the curve y = a²(et/x + e-x/a) is

What is the equation of the curve on which the tangents drawn from the origin to the curve y = cos x have their points of contact?

For the parabola y² = 4ax, the ratio of the subtangent to the abscissa is

If at each point of the curve y = x³ - ax² + x + 1, the tangent is inclined at an acute angle with the positive direction of the x-axis, then

What is the geometrical significance of the derivative of a function at a point?

If the function y = f(x) is increasing in an interval, then its derivative f'(x) in that interval is

The maximum or minimum value of a function occurs at a point where the

What is the rate of change of the function y = x³ - 3x² + 2x + 1 at x = 1?