Question

Determine the relation of the ellipse and x2+ 4y2=32 the line 2x+y-1

Answer 1

Given  : x² + 4y² = 32  , 2x+y-1=0

To Find : Points of intersections

Solution:

x² + 4y² = 32

2x + y - 1 = 0

=> y = 1 - 2x

x² + 4y² = 32

x² + 4(1-2x)² = 32

=> x² + 4(1  + 4x² - 4x) = 32

=> x²  + 4 + 16x²  - 16x = 32

=> 17x²  - 16x  - 28 = 0

=> x  = (16 ± √16² - 4(17)(-28) )/2(17)

=> x = (16 ± 12√15 )/2(17)

=> x = (8  ± 6√15)/17

y = 1 - 2x

=> y  = 1  - 2 ( (8  ± 6√15)/17)

=> y  =    (17 -  (16  ± 12√15) )/ 17

Intersection Points are :

 (8 +  6√15)/17  ,   (1  -  12√15)/17 )

 (8 -  6√15)/17  ,     (1 +  12√15)/17 )

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