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Find a point on the hyperbola x ^ 2 / 16-y ^ 2 / 9 = 1, so that the distance between the point and the left focus is equal to twice the distance between the point and the right focus
Given the hyperbolic equation x ^ 2 / 16-y ^ 2 / 9 = 1, then its focal coordinates are left m (- 5,0) and right n (5,0)
Let one point be p (x, y)
[PM]^2=(X+5)^2+Y^2:
[PN]^2=(X-5)^2+Y^2
And [PM] = 2 [PN]
So there are: 3x ^ 2-50x + 3 * 25 + 3Y ^ 2 = 0
Simultaneous hyperbolic equations,
3X^2-50X+3*25+27*(X^2-16)/16=0
(I can't calculate it well, you can calculate it. Get the value of X, bring in the hyperbola x ^ 2 / 16-y ^ 2 / 9 = 1, get y)
OK, point P coordinates are available
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