Home
Class 12
MATHS
Find the point on the curve y = (x - 2)^...

Find the 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).

Text Solution

Verified by Experts

Equation of the curve is,
`y = (x-2)^2`
`:. dy/dx = 2(x-2)`
`:.` Slope of the tangent`(m_1) = dy/dx = 2(x-2)`
Now, slope of the chord joining points `(2,0)` and `(4,4) = (4-0)/(4-2) = 2`
As, chord is parallel to the tangent, so their slopes will be equal.
`:. 2(x-2) = 2`
`=>x = 3`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

Find a point on the curve y=(x-2)^(2) at which the the tangent is parallel to the chord joining the points (2, 0) and (4, 4).

Find the points on the curve y=(x-2)^2 at which the tangents are parallel to the chord joining the points (2,0) and (4,4) .

Find the points on the curve y=x^(3)-3x at which the tangents are parallel to the chord joining the points (1,-2) and (2,2) .

Find the point on the curve y=2x^2-6x-4 at which the tangent is parallel to the x-axis.

Find the point on the curve y = 2x^(2) - 6x - 4 at which the tangent is parallel to the x-axis

Using Lagrange's mean-value theorem, find a point on the curve y = x^(2) , where the tangent is parallel to the line joining the points (1, 1) and (2, 4)

Find a point on the curve y = x^(3) , where the tangent to the curve is parallel to the chord joining the points (1, 1) and (3, 27)

Determine the points on the curve 2y = (3 - x^(2)) at which the tangent is parallel to the line x + y = 0

Find a point on the curve y=x^(2)+x, where the tangent is parallel to the chord joining (0,0) and (1,2).