9.
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Hi there!
Parabola x² = 12y
→ x² = 4ay
→ 4a = 12
→ a = 12÷4
→ a = 3
So, the co-ordinates of the focus is:-
S(0,a)=(0,3)
→ Let AB be the latus rectum of the given parabola.
→ Coordinates of end-points of latus rectum are (-2a,a), (2a,a)
→ Coordinates of A are (-6,3), while B's coordinates are (6,3).
→ ∆OAB are O(0,0), A(-6,3), B(6,3)
Area of ∆OAB is :-
(<em>Solving part attached as image</em>)
=> <u>1</u><u>8</u><u> </u><u>unit</u>² is the required answer.
Answer:
<h2>There are 9 ducks and 3 swans in the pond.</h2>Step-by-step explanation:
According to the problem, the number of swans in the pond is equal to the square root of the number of ducks, this can be expressed as
Where represents the number of ducks in the pond.
If the total number of swans and ducks is 12, the expression would be
Now, we replace the first equation in the second one
Then, we elevate each side to the square power
Using a calculator, the roots are 9 and 16.
Let's evaluate each value.
For ,
, and
, which is true.
For ,
, and
, which is false.
Therefore, there are 9 ducks and 3 swans in the pond.