Information Given:
A children’s park has a circular garden as shown in the figure with DC and AB representing x and y-axis respectively. AB and CD are two cemented walkways of length 70 m each. Areas marked as AEOF and BGOH are flower beds whereas ECGO and FDHO are covered with grass. FOE and HOG are parabolas with focus (0, 6) and (0, −6) respectively.
Based on the information given above answer the questions.
The equations of the curves FOE and HOG are respectively:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(x^2=24y\) and \(x^2=-24y\)
Both parabolas have their vertex at the origin O and their focus on the y-axis, so they are of the form \(x^2 = 4ay\) (opening upwards, focus (0, a)) or \(x^2 = -4ay\) (opening downwards, focus (0, −a)).
FOE: focus (0, 6), so a = 6:
\(x^2 = 4(6)y = 24y\)
HOG: focus (0, −6), so a = 6 and it opens downwards:
\(x^2 = -24y\)