Let point (x, y) be any point on the graph, than the distance between (x, y) and the focus (3, 6) is sqrt((x - 3)^2 + (y - 6)^2) and the distance between (x, y) and the directrix, y = 4 is |y - 4|
Thus sqrt((x - 3)^2 + (y - 6)^2) = |y - 4|
(x - 3)^2 + (y - 6)^2 = (y - 4)^2
x^2 - 6x + 9 + y^2 - 12y + 36 = y^2 - 8y + 16
x^2 - 6x + 29 = -8y + 12y = 4y
(x - 3)^2 + 20 = 4y
y = 1/4(x - 3)^2 + 5
Required answer is f(x) = one fourth (x - 3)^2 + 5
Answer:
circle question: 69.66
the other question: 66.8
Step-by-step explanation:
For the circle question:
the circle is inscribed in the square, so the diameter of the circle = side of the square
so we need to find the area of square and circle
then do this
square area - circle area
square area(side×side) = 324
circle area(pi×r^2)≈254.469
so shaded region = 69.66
__________
the other question:
we need to find the area of triangle and the area of the rectangle and add them together
A of Triangle (1/2×base×hight) = 34.32
A of rectangle (width × length) = 31.92
add them, so the answer will be = 66.8
