r(x)=(x-a)^2+(x+a)^2
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r(x) = (x + a)² + (x - a)²
= x² + a² + 2ax + x² + a² - 2ax
= 2(x² + a²)
this is the equation of parabola .
in which
focus : ( 0, 2a² + 1/8)
vertex : ( 0, 2a²)
semi - axis length : 1/8
focal parameter : 1/4
eccentricity : 1
directrix : y = 2a² - 1/8
see the figure , I gave 3D graph of given polynomial .
= x² + a² + 2ax + x² + a² - 2ax
= 2(x² + a²)
this is the equation of parabola .
in which
focus : ( 0, 2a² + 1/8)
vertex : ( 0, 2a²)
semi - axis length : 1/8
focal parameter : 1/4
eccentricity : 1
directrix : y = 2a² - 1/8
see the figure , I gave 3D graph of given polynomial .
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