For any real number t , the point 8 t 1 + t 2 , 4 1 - t 2 1 + t 2 lies on a/an

For any real number t, the point 8t1+t2,41-t21+t2 lies on a/an
  1. Circle of radius 2
  2. Circle of radius 4
  3. Ellipse with 4 as its major axis length
  4. Ellipse with 4 as its minor axis length

Solution

Let,

x=8t1+t2 .......1

And y=41-t21+t2 ......2

Now squaring and adding both the equation we get,

x2+y2=64t2+161-t221+t22

⇒x2+y2=161-t22+4t21+t22

⇒x2+y2=161+t221+t22

⇒x2+y2=16

Hence point lie on the circle of radius 4

Asked in: AP EAMCET 2022 (04 Jul Shift 2)

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