Let H : x 2 a 2 - 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 2 + 14 . If the eccentricity H is 11 2 , then value of a 2 + b 2 is equal to ______.

Question

Let H : x 2 a 2 - y 2 b 2 = 1 , a &#62; 0 , b &#62; 0 , be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is 4 2 2 + 14 . If the eccentricity H is 11 2 , then value of a 2 + b 2 is equal to ______.

Quantrex Academy · Accepted Answer

Correct answer: 0

Given x 2 a 2 - y 2 b 2 = 1 , 2 a + 2 b = 4 2 2 + 14 and e = 11 2 We know e 2 = 1 + b 2 a 2 &#8658; 11 4 = 1 + b 2 a 2 &#8658; b 2 = 7 4 a 2 &#8756; x 2 a 2 - y 2 7 2 a 2 = 1 Now 2 a + 2 &#183; 7 a 2 = 4 2 2 + 14 a 2 + 7 = 4 2 2 + 7 a = 4 2 &#8658; a 2 = 32 b 2 = 7 4 &#215; 16 &#215; 2 = 56 Hence a 2 + b 2 = 88

Let H : x 2 a 2 - 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 2 + 14 . If the eccentricity H is 11 2 , then value of a 2 + b 2 is equal to ______.

Correct answer

Step-by-step solution

More from Hyperbola

Let H : x 2 a 2 - y 2 b 2 = 1 , a &#62; 0 , b &#62; 0 , be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is 4 2 2 + 14 . If the eccentricity H is 11 2 , then value of a 2 + b 2 is equal to ______.

Correct answer

Step-by-step solution

More from Hyperbola

Let H : x 2 a 2 - 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 2 + 14 . If the eccentricity H is 11 2 , then value of a 2 + b 2 is equal to ______.