Advertisements
Advertisements
प्रश्न
Find the slope of the normal to the curve x = acos3θ, y = asin3θ at `theta = pi/4`
Advertisements
उत्तर
It is given that x = acos3θ and y = asin3θ.

APPEARS IN
संबंधित प्रश्न
The equation of tangent at (2, 3) on the curve y2 = ax3 + b is y = 4x – 5. Find the values of a and b.
Find the equation of tangents to the curve y= x3 + 2x – 4, which are perpendicular to line x + 14y + 3 = 0.
Show that the equation of normal at any point t on the curve x = 3 cos t – cos3t and y = 3 sin t – sin3t is 4 (y cos3t – sin3t) = 3 sin 4t
Find the slope of the tangent to the curve y = 3x4 − 4x at x = 4.
Find the slope of the tangent and the normal to the following curve at the indicted point \[y = \sqrt{x^3} \text { at } x = 4\] ?
Find the slope of the tangent and the normal to the following curve at the indicted point x = a (θ − sin θ), y = a(1 − cos θ) at θ = −π/2 ?
Find the slope of the tangent and the normal to the following curve at the indicted point y = (sin 2x + cot x + 2)2 at x = π/2 ?
Find the equation of the tangent and the normal to the following curve at the indicated point y = x4 − bx3 + 13x2 − 10x + 5 at (0, 5) ?
Find the equation of the tangent and the normal to the following curve at the indicated point y = x2 + 4x + 1 at x = 3 ?
Find the equation of the tangent and the normal to the following curve at the indicated point y2 = 4ax at \[\left( \frac{a}{m^2}, \frac{2a}{m} \right)\] ?
Find the equation of the tangent and the normal to the following curve at the indicated points x = asect, y = btant at t ?
Find the equation of the tangent line to the curve y = x2 + 4x − 16 which is parallel to the line 3x − y + 1 = 0 ?
Find an equation of normal line to the curve y = x3 + 2x + 6 which is parallel to the line x+ 14y + 4 = 0 ?
Find the equation of a normal to the curve y = x loge x which is parallel to the line 2x − 2y + 3 = 0 ?
Find the equation of the tangent line to the curve y = x2 − 2x + 7 which perpendicular to the line 5y − 15x = 13. ?
Find the equations of all lines having slope 2 and that are tangent to the curve \[y = \frac{1}{x - 3}, x \neq 3\] ?
Find the equation of the tangent to the curve x = sin 3t, y = cos 2t at
\[t = \frac{\pi}{4}\] ?
The angle between the curves y2 = x and x2 = y at (1, 1) is ______________ .
The equation of the normal to the curve 3x2 − y2 = 8 which is parallel to x + 3y = 8 is ____________ .
The angle of intersection of the curves y = 2 sin2 x and y = cos 2 x at \[x = \frac{\pi}{6}\] is ____________ .
Any tangent to the curve y = 2x7 + 3x + 5 __________________ .
Find the equation of tangents to the curve y = cos(x + y), –2π ≤ x ≤ 2π that are parallel to the line x + 2y = 0.
Find the equation of tangent to the curve y = x2 +4x + 1 at (-1 , -2).
Show that the equation of normal at any point on the curve x = 3cos θ – cos3θ, y = 3sinθ – sin3θ is 4 (y cos3θ – x sin3θ) = 3 sin 4θ
Find the condition that the curves 2x = y2 and 2xy = k intersect orthogonally.
The equation of normal to the curve 3x2 – y2 = 8 which is parallel to the line x + 3y = 8 is ______.
The two curves x3 – 3xy2 + 2 = 0 and 3x2y – y3 – 2 = 0 intersect at an angle of ______.
The distance between the point (1, 1) and the tangent to the curve y = e2x + x2 drawn at the point x = 0
Find a point on the curve y = (x – 2)2. at which the tangent is parallel to the chord joining the points (2, 0) and (4, 4).
Tangents to the curve x2 + y2 = 2 at the points (1, 1) and (-1, 1) are ____________.
If the tangent to the curve y = x + siny at a point (a, b) is parallel to the line joining `(0, 3/2)` and `(1/2, 2)`, then ______.
An edge of variable cube is increasing at the rate of 3 cm/s. The volume of the cube increasing fast when the edge is 10 cm long is ______ cm3/s.
If the curves y2 = 6x, 9x2 + by2 = 16, cut each other at right angles then the value of b is ______.
Two vertical poles of heights, 20 m and 80 m stand apart on a horizontal plane. The height (in meters) of the point of intersection of the lines joining the top of each pole to the foot of the other, From this horizontal plane is ______.
The normals to the curve x = a(θ + sinθ), y = a(1 – cosθ) at the points θ = (2n + 1)π, n∈I are all ______.
The normal of the curve given by the equation x = a(sinθ + cosθ), y = a(sinθ – cosθ) at the point θ is ______.
If m be the slope of a tangent to the curve e2y = 1 + 4x2, then ______.
If the tangent to the conic, y – 6 = x2 at (2, 10) touches the circle, x2 + y2 + 8x – 2y = k (for some fixed k) at a point (α, β); then (α, β) is ______.
