Q116 / 160 · AP EAMCET 2020 (18 Sep Shift 2) · Mathematics

The co-ordinates of the focus of the parabola \((x+3)^2=2(y-5)\) is

  • A
    \(\left(\frac{-5}{2}, 5\right)\)
  • Correct answer
    B
    \(\left(-3, \frac{11}{2}\right)\)
  • C
    \(\left(3, \frac{-11}{2}\right)\)
  • D
    \(\left(0, \frac{1}{2}\right)\)

Solution

\(\begin{aligned} & (x+3)^2=2(y-5) \\ & \therefore \quad \text {Vertex }=(-3,5), a=\frac{1}{2} \\ & \therefore \text {Focus }(s)=\left(-3,5+\frac{1}{2}\right)=\left(-3, \frac{11}{2}\right) \end{aligned}\) Hence, option (b) is correct.

Hence, the correct answer is option: 'B'.

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