Advertisements
Advertisements
Question
Find the point on the curve y = x2 – 5x + 4 at which the tangent is parallel to the line 3x + y = 7
Advertisements
Solution
y = x2 – 5x + 4
Differentiating w.r.t. ‘x’
Slope of the tangent `("d")/("d"x)` = 2x – 5
Given line 3x + y = 7
Slope of the line = `- 3/1` = – 3
Since the tangent is parallel to the line, their slopes are equal.
∴ ("d"y)/("d"x)` = – 3
⇒ 2x – 5 = – 3
2x = 2
x = 1
When x = 1, y = (1)2 – 5(1) + 4 = 0
∴ Point on the curve is (1, 0).
APPEARS IN
RELATED QUESTIONS
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. How long does the camera fall before it hits the ground?
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. Find the total distance travelled by the particle in the first 4 seconds
A stone is dropped into a pond causing ripples in the form of concentric circles. The radius r of the outer ripple is increasing at a constant rate at 2 cm per second. When the radius is 5 cm find the rate of changing of the total area of the disturbed water?
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 tangent and normal to the following curves at the given points on the curve
y = x4 + 2ex at (0, 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 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
Show that the two curves x2 – y2 = r2 and xy = c2 where c, r are constants, cut orthogonally
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:
Find the point on the curve 6y = x3 + 2 at which y-coordinate changes 8 times as fast as x-coordinate is
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:
The tangent to the curve y2 – xy + 9 = 0 is vertical when
Choose the correct alternative:
Angle between y2 = x and x2 = y at the origin is
Choose the correct alternative:
The maximum slope of the tangent to the curve y = ex sin x, x ∈ [0, 2π] is at
