Find the whole area included between the curvex2y2=a2(y2–x2)and its asymptotes. It is of formλa2.Find value ofλ.Correct answer is '4'. Can you explain this answer?

Question

Find the whole area included between the curvex2y2=a2(y2&ndash;x2)and its asymptotes. It is of form&lambda;a2.Find value of&lambda;.Correct answer is '4'. Can you explain this answer?

Answer

To find the whole area included between the curve x^2y^2 = a^2(y^2), we can rewrite the equation as x^2 = a^2.

Taking the square root of both sides, we have x = ±a.

Therefore, the curve is composed of two vertical lines at x = a and x = -a.

The area included between the curve is the area of a rectangle with height 2a (from y = -a to y = a) and width 2a (from x = -a to x = a).

So, the whole area included between the curve is (2a)(2a) = 4a^2.

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