Question

A curve is defined by the equation x^2 + y^2 = xy + 12. There are two points where the tangent to curve has the equation x = k, k E R Find the coordinates of the two points.​

Answer 1

Step-by-step explanation:

Question

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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).

Medium

Solution

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y=(x−2)

2

dx

dy

=

dx

d((x−2)

2

)

=2(x−2)

∴ slope of tangent =2x−4

Slope of line joining (2,0) and (4,4) =

4−2

4−0

=2

The tangent is parallel to this line

∴ their slopes are equal

2x−4=2 ⇒2x=6

∴x=3

and y=(3−2)

2

=1

Thus the point is (3,1)