Question
Mon March 15, 2010 By:

Parametric equations

Expert Reply
Mon March 15, 2010

(c) a parabola,

Add the two given equations,

x+y = 2(t2+1)

t2+1 = (x+y)/2  ... (1)

Subtract the given two equations,

t = (x-y)/2  

Put this t into (1),

(x-y)2/22 + 1 = (x+y)/2

x2 - 2xy + y2 + 4 = 2x+2y

x2 - 2xy + y2 - 2x - 2y + 4 = 0 

Comparing this with the standard form,

Ax2 +  Bxy + Cy2 + Dx + Ey + F = 0

we find, B2 - 4AC = 0, which tells us it's a parabola.

Regards,

Team,

TopperLearning. 

 

 

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