A circular garden at the local park has a circumference of 942 feet. What is the radius of the garden in feet? (use 3.14 to app
2 answers:
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If your directrix is a "y=" line, that means that the parabola opens either upwards or downwards (as opposed to the left or the right). Because it is in the character of a parabola to "hug" the focus, our parabola opens upwards. The vertex of a parabola sits exactly halfway between the directrix and the focus. Since our directrix is at y = -2 and the focus is at (1, 6) AND the parabola opens upward, the vertex is going to sit on the main transversal, which is also the "line" the focus sits on. The focus is on the line x = 1, so the vertex will also have that x coordinate. Halfway between the y points of the directrix and the focus, -2 and 6, respectively, is the y value of 2. So the vertex sits at (1, 2). The formula for this type of parabola is where h and k are the coordinates of the vertex and p is the DISTANCE that the focus is from the vertex. Our focus is 4 units from the vertex, so p = 4. Filling in our h, k, and p:
. Simplifying a bit gives us
. We can begin to isolate the y by dividing both sides by 16 to get
. Then we can add 2 to both sides to get the final equation
, choice 4 from above.
Area of a circle is 
. The first one, a, the radius squared is 8*8=64. So 
. If you multiply in pi as 3.14, you'll have 200.96 square inches. The second one, b, the radius squared is 10*10=100. So 
square kilometers. If you multiply in pi as 3.14 you'll have 314 square kilometers. The third one, c, the radius squared is 14*14=196. So 
. Or you could multiply in pi as 3.14 to get 615.44 yd squared. For the last one, d, the radius squared is 22*22=484 cm. Therefore, 
, or multiply in 3.14 for pi to get 1519.76 cm squared. There you go!