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AP EAMCET20224 Jul 2022Evening ShiftMathematicsCircleActual

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

Options

  1. ACircle of radius 2
  2. BCircle of radius 4
  3. CEllipse with 4 as its major axis length
  4. DEllipse with 4 as its minor axis length

Correct answer

B. Circle of radius 4

Step-by-step solution

Let, x = 8 t 1 + t 2   . . . . . . . 1 And y = 4 1 - t 2 1 + t 2   . . . . . . 2 Now squaring and adding both the equation we get, x 2 + y 2 = 64 t 2 + 16 1 - t 2 2 1 + t 2 2 ⇒ x 2 + y 2 = 16 1 - t 2 2 + 4 t 2 1 + t 2 2 ⇒ x 2 + y 2 = 16 1 + t 2 2 1 + t 2 2 ⇒ x 2 + y 2 = 16 Hence point lie on the circle of radius 4

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