It is proved that the slope product of AP and BP is colonization
First, the rectangular coordinate system is established
Let P (x, y) a (- A, 0) B (a, O)
Then kPa * kbp = Y / (x + a) * y / (x-a) = the square of Y / (the square of x-a)
Let the equation of the ellipse be the square of X divided by the square of a + the square of Y divided by the square of B = 1
If y is represented by x a B, then the square of y = (a times B - B times x) divided by A
By taking the above formula into the first equation, we can get that the slope product is equal to minus B divided by A
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