Question

Draw the rough sketch of \( 4 x^{2}+16 y^{2}=16 \). Find the area enclosed by the curve in the first quadrant.

Answer 1

\(4x^2 + 16y^2 = 16\)

⇒ \(\frac{x^2}4 + \frac{y^2}1 = 1\)

which is equation of an ellipse whose centre is (0, 0) and major axis is x-axis.

Enclosed area in first quadrant \(= \frac {\pi ab}4\)

\(= \frac{\pi \times 2\times 1}4\)

\(= \frac \pi 2\) sq. units