Let <math><mrow><mi>H</mi><mo>:</mo><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><mo>,</mo><mtext> </mtext><mtext> </mtext><mi>a</mi><mo>></mo><mn>0</mn><mo>,</mo><mtext> </mtext><mtext> </mtext><mi>b</mi><mo>></mo><mn>0</mn><mo>,</mo></mrow></math> be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is <math><mrow><mn>4</mn><mrow><mo>(</mo><mrow><mn>2</mn><mroot><mrow><mn>2</mn></mrow><mrow></mrow></mroot><mo>+</mo><mroot><mrow><mn>1</mn><mn>4</mn></mrow><mrow></mrow></mroot></mrow><mo>)</mo></mrow><mo>.</mo></mrow></math> If the eccentricity H is <math><mrow><mfrac><mrow><mroot><mrow><mn>1</mn><mn>1</mn></mrow><mrow></mrow></mroot></mrow><mrow><mn>2</mn></mrow></mfrac><mo>,</mo></mrow></math> then the value of a2 + b2 is equal to………….

Given 2a + 2b = 4 (22+14)=42 (2+7)b2=a2 (114−1)4b2 = 7a2b = 72a

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Let $H : \frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1, a > 0, b > 0,$ be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is $4 (2 \sqrt[]{2} + \sqrt[]{14}) .$ If the eccentricity H is $\frac{\sqrt[]{11}}{2},$ then the value of a² + b² is equal to………….

2 Views | Posted 2 months ago

Answered by

alok kumar singh | Contributor-Level 10

2 months ago

Given 2a + 2b = $4 (2 \sqrt[]{2} + \sqrt[]{14})$

$= 4 \sqrt[]{2} (2 + \sqrt[]{7})$

$b^{2} = a^{2} (\frac{11}{4} - 1)$

4b2 = 7a2

b = $\frac{\sqrt[]{7}}{2} a$

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