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AP EAMCET202120 Aug 2021Evening ShiftMathematicsParabolaActual

The point of intersection of the latus rectum and axis of the parabola y 2 + 4 x + 2 y - 8 = 0 is

Options

  1. A9 4 , - 1
  2. B5 4 , - 1
  3. C7 2 , 5 2
  4. D- 5 4 , 1

Correct answer

B. 5 4 , - 1

Step-by-step solution

The point of intersection of the latus rectum and axis of the parabola y 2 + 4 x + 2 y - 8 = 0 is the focus of the parabola. y 2 + 4 x + 2 y - 8 = 0 ⇒ y 2 + 2 y + 1 = - 4 x + 8 + 1 ⇒ y + 1 2 = 4 - 1 x - 9 4 We know that the focus of the parabola y - k 2 = 4 a x - h is S ≡ a + h , k . So, the focus of the given parabola is S ≡ - 1 + 9 4 , - 1 ≡ 5 4 , - 1 .

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