For real numbers a, b(a > b > 0), let

$Area\left\{\left(x,y\right):x^2+y^2\le a^{2}and\frac{x^2}{a^2}+\frac{y^2}{b^2}\ge 1\right\}=30\pi and$

$Area\left\{\left(x,y\right):x^2+y^2\ge b^{2}and\frac{x^2}{a^2}+\frac{y^2}{b^2}\le 1\right\}=18\pi$

Then the value of (a – b)² is equal to

<p>Given a &gt; b</p><p>Area common to x2 + y2&nbsp;<math><mrow><mo>≤</mo><msup><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msup><mtext> </mtext><mtext> </mtext><mi>a</mi><mi>n</mi><mi>d</mi><mtext> </mtext><mtext> </mtext><mfrac><mrow><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><msup><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo>+</mo><mfrac><mrow><msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow><mrow><msup><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfrac><mo>≤</mo><mn>1</mn></mrow></math></p><p>is&nbsp;<math><mrow><mi>π</mi><msup><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mi>π</mi><mi>a</mi><mi>b</mi><mo>=</mo><mn>3</mn><mn>0</mn><mi>π</mi><mtext> </mtext><mtext> </mtext><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mrow><mo> (</mo><mrow><mi>i</mi></mrow><mo>)</mo></mrow></mrow></math></p><p>Similarly&nbsp;<math><mrow><mi>π</mi><mi>a</mi><mi>b</mi><mo>−</mo><mi>π</mi><msup><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>1</mn><mn>8</mn><mi>π</mi><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>.</mo><mrow><mo> (</mo><mrow><mi>i</mi><mi>i</mi></mrow><mo>)</mo></mrow></mrow></math></p><p>Equation (i) and equation (ii)&nbsp;<math><mrow><mfrac><mrow><mi>a</mi></mrow><mrow><mi>b</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></math></p><p>Equation (i) + equation (ii)&nbsp;<math><mrow><msup><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><msup><mrow><mi>b</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>4</mn><mn>8</mn></mrow></math></p><p>a²= 75, b² = 27</p>

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