Question

if a = (x.y)(x²+y²=25) and B=(x.y)(x²+9y²=144) then A & B contains

Answer 1

Given : A = (x,y)(x²+y²=25) and B=(x,y)(x²+9y²=144)

To find : A ∩ B

Solution:

x²  + y ²  = 25

x²  + 9y²  = 144

=> 8y²  = 119

=> y² = 119/8

=> y  = ± √ 119/ 2√2

Substitute y² = 119/8  

in     x²  + y ²  = 25

=> x²  + 119/8  = 25

=> x² = 81/8

=> x  = ± 9/2√2

4 Possible points area

(   9/2√2 ,  √ 119/ 2√2 )   ,

(   9/2√2 ,  -√ 119/ 2√2 )  

(   -9/2√2 ,  √ 119/ 2√2 )  

(   -9/2√2 ,  -√ 119/ 2√2 )  

A ∩ B  = 4

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