Advertisements
Advertisements
प्रश्न
Find the slope of the tangent to the following curves at the respective given points.
x = a cos3t, y = b sin3t at t = `pi/2`
Advertisements
उत्तर
x = a cos3t, y = b sin3t
Differenriating w.r.t. ‘t’
`("d"x)/("dt"` = – 3a cos2t sin t
`("d"y)/("dt"` = 3b sin2t sin t
`("d"y)/("d"x) = (("d"y)/("dt"))/(("d"x)/("dt"))`
= `(3"b" sin^2 "t" cos "t")/(-3"a" cos^2"t" sin"t"`
= `- "b"/"a" sin"t"/cos"t"`
= `- "b"/"a" tan "t"`
Slope of the tangent `(("d"y)/("d"x))_(("t" = pi/2))`
= `- "b"/"a" tan i/2 = oo`
APPEARS IN
संबंधित प्रश्न
A particle moves along a straight line in such a way that after t seconds its distance from the origin is s = 2t2 + 3t metres. Find the instantaneous velocities at t = 3 and t = 6 seconds
A camera is accidentally knocked off an edge of a cliff 400 ft high. The camera falls a distance of s = 16t2 in t seconds. What is the instantaneous velocity of the camera when it hits the ground?
If the mass m(x) (in kilograms) of a thin rod of length x (in metres) is given by, m(x) = `sqrt(3x)` then what is the rate of change of mass with respect to the length when it is x = 3 and x = 27 metres
A beacon makes one revolution every 10 seconds. It is located on a ship which is anchored 5 km from a straight shoreline. How fast is the beam moving along the shoreline when it makes an angle of 45° with the shore?
A police jeep, approaching an orthogonal intersection from the northern direction, is chasing a speeding car that has turned and moving straight east. When the jeep is 0.6 km north of the intersection and the car is 0.8 km to the east. The police determine with a radar that the distance between them and the car is increasing at 20 km/hr. If the jeep is moving at 60 km/hr at the instant of measurement, what is the speed of the car?
Find the point on the curve y = x2 – 5x + 4 at which the tangent is parallel to the line 3x + y = 7
Find the points on curve y = x3 – 6x2 + x + 3 where the normal is parallel to the line x + y = 1729
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
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
Choose the correct alternative:
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
Choose the correct alternative:
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
Choose the correct alternative:
The slope of the line normal to the curve f(x) = 2 cos 4x at x = `pi/12` is
Choose the correct alternative:
Angle between y2 = x and x2 = y at the origin is
