- #1

vitaly

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1. Write the equation of the hyperbola, x^2 + 4xy + y^2 - 12 = 0, in standard form.

Okay, I know the formula needs to be x^2/a^2 - y^2/b^2 = 1, but I can't get it into that form... Is there a possibility that there is a typo. But, on the other hand, I checked to see if this is indeed a hyperbola, so I used the

B^2 - 4AC rule, and the result was greater than zero. That should mean the equation is a hyperbola or two intersecting lines. The problem is only getting it into standard form. Any ideas?

2. An arch in a cathedral has the shape of the top half an ellipse and is 40 feet wide and 12 feet high from the center from the floor. Find the height of the arch at 10 feet from the center?

I tried a lot of things, in desperation. Unfortunately, there are no examples in my book, and I couldn't find any online. I tried putting it into standard form of x^2/a^2 + y^2/b^2 = 1, but nothing worked. I can position the ellipse to be in the center, so a possible point would be (0,12), but I don't know where to go from there. All help is appreciated.