35. Find the area of the region {(x, y) : y2 ≤ 4x, 4x2 + 4y2 ≤ 9}.

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Vishal Baghel | Contributor-Level 10

8 months ago

The given equation of curve $y^{2} \leq 4 x$ i.e, $y^{2} = 4 x$ - (1) is a parabola and

$4 x^{2} + 4 y^{2} \leq 9 \Rightarrow x^{2} + y^{2} \leq \frac{9}{4} \Rightarrow x^{2} + y^{2} = {(\frac{3}{2})}^{2}$ - (2) is a circle

With centre (0,0)and radius

Solving (1) and (2) for x and y,

$\begin{array}{l} x^{2} + 4 x = \frac{9}{4} \\ = x^{2} + 4 x - \frac{9}{4} = 0 \\ = 4 x^{2} + 16 x - 9 = 0 \end{array}$

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