Q. 234.0( 4 Votes )

# Find the area of

Answer : As we know that: For a given ellipse we can give the coordinates of a point on the given ellipse by (acos θ, bsin θ)

From figure we can say that length of rectangle = 2a cosθ

Note: In reference to figure - (taking z = θ)

And breadth of inscribed rectangle = 2b sinθ

Let A be the area of rectangle inscribed.

A = 4ab sinθ cos θ = 2ab sin 2θ

We need to maximise the area.  4ab cos 2θ = 0

cos 2θ = 0

θ = π/4

Clearly, And θ = π/4 is the point of maxima.

Hence area of the greatest rectangle that can be inscribed in the given ellipse is given by

A = 2ab sin(2×π/4) = 2ab.

OR

Given equation is 3x2 – y2 = 8.

To find the equation of tangent we need to find the slope first and the slope is given by the value of derivative at that point.

As, 3x2 – y2 = 8

Differentiating both sides w.r.t x, we get –    As slope comes to be infinite line is parallel to y – axis

Given that it passes through (4/3,0)

line parallel to y-axis and passing through (4/3,0) is

x = 4/3 Rate this question :

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