y^2 x^2
___ - _____ = 1 (1)
4 2
y^2 = 8(x + 1) (2)
Sub (2) into (1) and we get that
8(x + 1) x^2
_______ - _____ = 1 Multiply this through by 4
4 2
8(x + 1) - 2x^2 = 4
8x + 8 - 2x^2 = 4 rearrange as
2x^2 - 8x - 4 = 0 divide through by 2
x^2 - 4x - 2 = 0
Using the quad formula
x = 4 ±√[ 4^2 - 4 (1) (-2) ] 4 ±√24 4 ±√[4*6] 4 ±2√6
______________________ = ________ = _________ = ______ = 2±√6
2 * 1 2 2 2
When x = 2 + √6 then we have that
y^2 = 8( 2 + √6 + 1)
y^2 = 8 ( 3 + √6) take both roots
y = ±√[ 8 (3 + √6) ]
y = ±2√[ 2 (3 + √6 ]
y = ±2√[6 + 2√6 ]
And when x = 2 -√6 we have that
y^2 = 8( 2 - √6 + 1) take both roots
y = ±√[ 8 ( 3 - √6) ]
y = ±2√[2(3 - √6) ]
y = ±2√[6 - 2√6 ]
So......
When x = 2 +√6....then y = 2√[6 + 2√6 ] and -2√[6 + 2√6 ]
When x = 2 - √6....then y = 2√[6 - 2√6 ] and -2√[6 - 2√6 ]
