# algebra

An ellipse and a hyperbola have the same foci, $A$ and $B$, and intersect at four points. The ellipse has major axis 50, and minor axis 40. The hyperbola has conjugate axis of length 20. Let $P$ be a point on both the hyperbola and ellipse. What is $PA \cdot PB$?

1. 👍
2. 👎
3. 👁
1. If you set up the curves as described, you have

x^2/25^2 + y^2/20^2 = 1
x^2/125 - y^2/100 = 1

They intersect at (±25√5/3,±40/3) so pick P to be one of those points and figure your answer.

1. 👍
2. 👎
2. Steve means the intersections are (±(25√5)/3,±(40)/3) if anyone is confused.
Focus 1 (A): (15, 0)
Focus 2 (B): (-15, 0)
P: ((25√5)/3,(40)/3)
The question is asking for the distance between P and A, and multiply that by the distance between P and B.
Distance between P and A: √(750 - 250√5)
Distance between P and B: √(750 + 250√5)
Our final answer is 500, which is correct.

1. 👍
2. 👎

## Similar Questions

1. ### Math

I am terrible at ellipse The base of an auditorium is in the form of an ellipse 200ft long and 100 ft wide. A pin dropped near one focus can clearly be heard at the other focus. Determine the distance between the foci to the

Find the equation of a hyperbola with foci of (0,8), and (0,-8) and Asymptotes of y=4x and y=-4x Please show work!!!

3. ### algebra

HYPERBOLA Q!! Find an equation for a horizontal hyperbola with vertices that are 20 units apart from each other and foci 30 units apart each other?? im lost on this any help is appreciated !!!

4. ### Calc

Oscar Corporation is planning to construct an elliptical gate at its headquarters. The width of the ellipse will be 5 feet across and its maximum height along the center will be 3 feet. The company wants to place two bright spots

1. ### precalculus

find an hyperbola equation with foci (0, +/-8) and asymptotes; y=+/-1/2x?

2. ### precalculus

Find the vertices, foci, and asymptotes of the hyperbola. 16x2 − 9y2 = 144

3. ### Math, precalculus

Write an equation for the hyperbola with vertices (7,5),(-5,5); foci (11,5),(-9,5)

4. ### math

An ellipse and a hyperbola have the same foci, $A$ and $B$, and intersect at four points. The ellipse has major axis 50, and minor axis 40. The hyperbola has conjugate axis of length 20. Let $P$ be a point on both the hyperbola

1. ### Trig

Find an equation for the hyperbola described. Foci at (-4,0) and (4,0); asymptote the line y= -x. Please explain the steps of this problem. My book does not get an example of this type of problem and I'm not having any luck

2. ### Algebra

What are the foci of the hyperbola with equation 16y^2-9x^2=144

3. ### Precalc

Find the standard form of the equation of the hyperbola with the given characteristics. foci: (±4, 0) asymptotes: y= +/- 3x

4. ### Math

1.) Write the standard form equation for the following Ellipse. Use the information given below. Foci: (0,0) and (4,0) 2.) Write the standard form equation for the following Hyperbola. Use the information below. Vertices (-2,1)