Advertisements
Advertisements
प्रश्न
Find the equations of the tangents to the curve y = `- (x + 1)/(x - 1)` which are parallel to the line x + 2y = 6
Advertisements
उत्तर
Curse is y = `(x + 1)/(x - 1)`
DIfferentiating w.r.t. 'x'
`("d"y)/("d"x) = ((x - 1)(1) - (x + 1)(1))/(x - 1)^2`
Slope of the tangent 'm'
= `(x - 1 - x - 1)/(x - 1)^2`
= `- 2/(x - 1)^2`
Given line is x + 2y = 6
Slope of the line = ` 1/2`
Since the tangent is parallel to the line, then the slope of the tangent is `- 1/2`
∴ `("d"y)/("d"x) = 2/(x 1)^2 = - 1/2`
(x – 1)2 = 4
x – 1 = ± 2
x = – 1, 3
When x = – 1, y = 0
⇒ point is (– 1, 0)
When x = 3, y = 2
⇒ point is (3, 2)
Equation of tangent with slope `- 1/2` and at the point (– 1, 0) is
y – 0 = `- 1/2(x + 1)`
2y = – x – 1
⇒ x + 2y + 1 = 0
Equation of tangent with slope ` 1/2` and at the point (3, 2) is 2
y – 2 = `- 1/2 (x - 3)`
2y – 4 = – x + 3
x + 2y – 7 = 0.
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 average velocity between 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?
A particle moves along a line according to the law s(t) = 2t3 – 9t2 + 12t – 4, where t ≥ 0. At what times the particle changes direction?
A particle moves along a line according to the law s(t) = 2t3 – 9t2 + 12t – 4, where t ≥ 0. Find the particle’s acceleration each time the velocity is zero
If the volume of a cube of side length x is v = x3. Find the rate of change of the volume with respect to x when x = 5 units
A ladder 17 metre long is leaning against the wall. The base of the ladder is pulled away from the wall at a rate of 5 m/s. When the base of the ladder is 8 metres from the wall. How fast is the top of the ladder moving down the wall?
A ladder 17 metre long is leaning against the wall. The base of the ladder is pulled away from the wall at a rate of 5 m/s. When the base of the ladder is 8 metres from the wall, at what rate, the area of the triangle formed by the ladder, wall, and the floor, is changing?
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`
Find the points on curve y = x3 – 6x2 + x + 3 where the normal is parallel to the line x + y = 1729
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 equations of the tangents to the curve y = 1 + x3 for which the tangent is orthogonal with the line x + 12y = 12
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:
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
Choose the correct alternative:
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
Choose the correct alternative:
The maximum slope of the tangent to the curve y = ex sin x, x ∈ [0, 2π] is at
