For real numbers a , b a > b > 0 , let Area x , y : x 2 + y 2 ≤ a 2 and x 2 a 2 + y 2 b 2 ≥ 1 = 30 π and Area x , y : x 2 + y 2 ≥ b 2 and x 2 a 2 + y 2 b 2 ≤ 1 = 18 π Then the value of a - b 2 is eq

Question

For real numbers a , b a &#62; b &#62; 0 , let Area x , y : x 2 + y 2 &#8804; a 2 and x 2 a 2 + y 2 b 2 &#8805; 1 = 30 &#960; and Area x , y : x 2 + y 2 &#8805; b 2 and x 2 a 2 + y 2 b 2 &#8804; 1 = 18 &#960; Then the value of a - b 2 is equal to _____.

Quantrex Academy · Accepted Answer

Correct answer: 0

We know that area of circle = &#960;r 2 ( r is radius of circle) and area of ellipse = &#960;ab (where a &#160; &#38; &#160; b are length of semi major and semi minor axis) Now given area between circle and ellipse &#8658; &#960; a 2 - &#960; a b = 30 &#960; .....(i) And &#8658; &#960; a b - &#960; b 2 = 18 &#960; ....(ii) On subtracting equation (i) - (ii), we get a - b 2 = a 2 - 2 a b + b 2 = 12 .

For real numbers a , b a > b > 0 , let Area x , y : x 2 + y 2 ≤ a 2 and x 2 a 2 + y 2 b 2 ≥ 1 = 30 π and Area x , y : x 2 + y 2 ≥ b 2 and x 2 a 2 + y 2 b 2 ≤ 1 = 18 π Then the value of a - b 2 is equal to _____.

Correct answer

Step-by-step solution

More from Area Under Curves

For real numbers a , b a &#62; b &#62; 0 , let Area x , y : x 2 + y 2 &#8804; a 2 and x 2 a 2 + y 2 b 2 &#8805; 1 = 30 &#960; and Area x , y : x 2 + y 2 &#8805; b 2 and x 2 a 2 + y 2 b 2 &#8804; 1 = 18 &#960; Then the value of a - b 2 is equal to _____.

Correct answer

Step-by-step solution

More from Area Under Curves

For real numbers a , b a > b > 0 , let Area x , y : x 2 + y 2 ≤ a 2 and x 2 a 2 + y 2 b 2 ≥ 1 = 30 π and Area x , y : x 2 + y 2 ≥ b 2 and x 2 a 2 + y 2 b 2 ≤ 1 = 18 π Then the value of a - b 2 is equal to _____.