IMPOSSIBLE math problem... you are a genius if you can answer this CORRECTLY !!!!!?

Question

Find the maximum area of a circle that is inscribed by the line y = 4 and the parabola y = x^2

There is no more information given about this problem.

these were extra credit problems that were given to us. I know the center cant be (0,2) because that would be too easy. Please help!!... THANK YOU!!!

Answer 1

i don't know how to figure out the max area of the circle but i can tell you that the area of the parabola inside the line is 10.667. this comes from a parabola being 2/3rds the area of the rectangle it is inscribed in, which is 4 units by 4 units thus making the area of the rectangle 16.

the circle part i don't really know but there must be some equation... maybe r^2=(x-h)^2+(y-k)^2, and you know that the center must lie on the y axis...

just throwin this out there. maybe it will spark something you've learned earlier. check your book for formulas.

Answer 2

y = x^2

Consider positive x:

x | 1 | 2 | 3 | 4
------------------------------
y | 1 | 4 | 9 | 16

Consider negative x:

x | -1 | -2 | -3 | -4
---------------------------------
y | 1 | 4 | 9 | 16

You can see in both cases that the y values become more positive as the x values increase in magnitude (the number regardless of the
sign), so the parabola opens up.

For y = -x^2, consider positive x:

x | 1 | 2 | 3 | 4
-----------------------------------
y | -1 | -4 | -9 | -16

Consider negative x:

x | -1 | -2 | -3 | -4
-----------------------------------
y | -1 | -4 | -9 | -16

You can see in both cases that the y values become more negative as the x values increase, so the parabola opens down.

Thus you can see that given the sign of a determines whether the parabola opens up or down. You can even get a feeling that only the
sign of a matters since:

-> a parabola with a not equal to 1 or -1 will just be a scaled version of the example, which will still grow faster as x gets larger (+ or -)

-> a parabola with b and c not zero will be a parabola that has a line added, but since the squared term grows much faster than the linear term, the squared term will dominate (as x gets really big only x^2 will matter), so the addition of the b and c will only change where the parabola is centered, not the direction it opens.

So to summarize:

a>0 => parabola opens up (concave up, like a bowl)

a<0 => parabola opens down (concave down, like an umbrella)

Answer 3

12.566 square units. the x axis is the bottom of the circle and y=4 is the top the radius is 2. (Pi)r^2 is the area of a circle.

Answer 4

ok - the circle is inside the parabola

2x = diameter

therefore the max area of circle is
x(squared) * pi

just name me

Wile E. Coyote
Genius - who changes his answers

Answer 5

well i have absolutly no idea..but have you considered maybe the problem really is impossible?

Answer 6

maybe that is the answer is impossible

Answer 7

wow im sorry i cant.