The parabola y2-4x-1 divides the disc x2-y2- 1 into two regions with areas A1 and A2- Then -A1-A2- equals-

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Area between Two Curves

The parabola ...

Question

The parabola $y^{2} = 4 x + 1$ divides the disc $x^{2} + y^{2} \leq 1$ into two regions with areas $A_{1}$ and $A_{2}$ . Then $| A_{1} - A_{2} |$ equals.

\frac{1}{3}

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\frac{2}{3}

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\frac{π}{4}

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\frac{π}{3}

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Solution

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y^{2} = 4 x + 1

x^{2} + y^{2} \leq 1

A_{1}

A_{2}

| A_{1} - A_{2} |

x = \frac{π}{4}

y = sin x, y = cos x

(0 \leq x \leq \frac{π}{2})

A_{1}

A_{2}

A_{1} : A_{2}

y^{2} = 4 x, x^{2} = 4 y

x = 4, y = 4

A_{1}, A_{2}, A_{3}

\frac{A_{1}}{A_{2}} + \frac{A_{2}}{A_{3}} + \frac{A_{3}}{A_{1}} =

p (θ), D (θ + \frac{π}{2})

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

y^{2} = x

x^{2} + y^{2} = 2 x

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