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?

PA.PB=600

Step-by-step explanation:

Given Data

Major axis=50

Minor axis=40

conjugate axis of length=20

P be a point on both the hyperbola and ellipse

PA.PB=?

Solution

Taken definition of ellipse

PA+PB=50

Minor axis of ellipse is 40 then a=25 and b=20

Which makes focal distance c=15

For hyperbola

2b is conjugate axis

2a is the transverse axis

So for this hyperbola 2b=20

                                     b=20/2

                                      b=10

and c=15

then

that makes

2a=10 Distance between vertices

If P is point

So for this hyperbola

|PA-PB|=10

We know for ellipse

PA+PB=50

Since

you can't solve x because it is 2 linear equation and you only have one equation