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the curve describes parametrically by x = t^2 +t+1 and y = t^2-t+1 represents A) STRAIGHT LINE B) ELLIPSE C) HYPERBOLA D) PARABOLA

the curve describes parametrically by x = t^2 +t+1 and y = t^2-t+1 represents
A) STRAIGHT LINE
B) ELLIPSE
C) HYPERBOLA
D) PARABOLA

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
148 Points
14 years ago

Hi raman

x = t^2 +t+1 and y = t^2-t+1

just simply aubtract

x-y =2t

or t=(x-y)/2

Nor put yalue of t in any one of above equation

y=[(x-y)/2]2 - (x-y)/2 +1

simplify

x2+y2 -2xy-2x-2y +4 =0

compair this equation with the general equation

Δ not equal to zero

and h2 -ab=0

so its represent parabola

 

Regards

 Badiuddin

 


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