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AP EAMCET201825 Apr 2018Morning ShiftMathematicsParabolaActual

For the parabola y 2 + 6 y - 2 x + 5 = 0 , match the items in List- I with the suitable item in List- II given below: List- I List- II I Vertex A - 3 2 , - 3 II Focus B 3 2 , - 3 III Equation of the directrix C 2 x + 5 = 0 IV Equation of the axis D 2 x + y + 3 = 0 E y + 3 = 0 F - 2 , - 3 The correct matching is

Options

  1. AI II III IV F A E C
  2. BI II III IV F A C E
  3. CI II III IV A B C D
  4. DI II III IV F A C D

Correct answer

B. I II III IV F A C E

Step-by-step solution

Given: y 2 + 6 y - 2 x + 5 = 0 ⇒ y + 3 2 = 2 x + 4 ⇒ y + 3 2 = 2 x + 2 The form: y - k 2 = 4 a x - h , where, the vertex is V h , k Therefore, Vertex ≡ - 2 , - 3 Now, 4 a = 2 ⇒ a = 1 2 Now, we know that focus lies at a distance a from the vertex of the parabola. Therefore, - 2 + a = - 2 + 1 2 = - 3 2 So, coordinates of focus are - 3 2 , - 3 Equation of directrix in standard form is x + a = 0 from the vertex. Therefore, equation of directrix is x = - 2 - 1 2 = - 5 2 or 2 x + 5 = 0 And, axes i

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