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A day full of math games & activities. Find one near you.
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)
Solution:
The slope of a line is nothing but the change in y coordinate with respect to the change in x coordinate of that line.
If a tangent is parallel to the chord joining the points (2, 0) and (4, 4)
Then, the slope of the tangent
= the slope of the chord.
Hence,
the slope of chord is (4 - 0)/(4 - 2)
= 4/2
= 2
Now, the slope of the tangent to the given curve is,
dy/dx
= 2(x - 2)
Since the slope of the tangent
= the slope of the chord.
Hence,
2(x - 2) = 2
⇒ x - 2 = 1
⇒ x = 3
When, x = 3
Then,
y = (3 - 2)2
= 1
Hence, the point on the curve is (3, 1)
NCERT Solutions Class 12 Maths - Chapter 6 Exercise 6.3 Question 8
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)
Summary:
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) is (3, 1)
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