# Homework Help: Analytic geometry: ellipse

1. May 21, 2012

### raven_claws

1. The problem statement, all variables and given/known data
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1. a hall that is 10 ft. wide has a ceiling that is a semi-ellipse. the ceiling is 10 ft high at the sides and 12 ft high in the center find its equation with the x axis horizontal and the origin at the center of the ellipse.

2. Relevant equations

x^2/a^2 + y^2/b^2 = 1

3. The attempt at a solution

The difference between the height at the ceiling and the sides is 12-10 = 2 ft. This is the value of b.

I assume that the vertices of the ellipse are 10 feet apart, the same as the width of the hall. This means that the major axis is 10 ft. Therefore, a = 10/2 =5.

The equation of the ellipse is x^2/25 + y^2/4 = 1

p.s. i think i got the right answer but i need a better solution.

1. The problem statement, all variables and given/known data

the point p1(x1,y1) lies outside the circle whose center is at (h,k) and whose radius is r. if T is the length of the tangent from p1 to the circle, prove that t2=(x1-h)^2+y1-k)^2-r^2

2. Relevant equations

(x-h)^2+(y-k)^2=r^2

3. The attempt at a solution

P (x1,y1) (x-h)^2+(y-k)^2=r^2

i used distance formula

P (x1,y1) to (x-h)^2+(y-k)^2-r^2=0

= (x1-h)^2+y1-k)^2-r^2