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Q.

Consider the parabola represented by the parametric equations x=t22t+2;y=t2+2t+2. Then which of the following is/are true?

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a

x+y=4 is tangent at vertex

b

Vertex of the parabola is (2, 2)

c

Length of latus rectum is 42

d

Focus of the parabola is (3, 3)

answer is A, B, C, D.

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Detailed Solution

x=t22t+2;   y=t2+2t+2

x+y=2(t2+2) and yx=4t

x+y2=(yx)216+2(yx)2=8(x+y4)

yx22=42x+y42

This is parabola for which y=x is axis,  x+y=4  is tangent at vertex and length of latus rectum is 42

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