Traditional Culture Encyclopedia - Photography major - Jining focus image photography
Jining focus image photography
Let |AF2|=t and |AB|=3x, then |BF 1|=4x, |AF 1|=5x,
According to the definition of hyperbola, | af1| | af2 | = | bf2 | | BF1| = 2a.
That is, 5x-t=(3x+t)-4x=2a, and the solution is t=3x and a = x.
∵| AB |: | BF1|: | AF1| = 3: 4: 5, so △ABF 1 is Rt△ with B as the right angle.
∴ cos ∠ BAF1= | ab || af1| = 35, and cos∠F2AF 1=-35 can be obtained.
△F2AF 1,| f 1 F2 | 2 = | af 1 | 2+| af2 | 2 | af 1 |? |AF2|cos∠F2AF 1
=25x2+9x2-2×5x×3x×(-35)=52x2, then |F 1F2|=2 13x.
So the eccentricity of this hyperbola is e=2c2a=2 13x2x= 13.
So choose: a
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