Through the right focus F of hyperbola x2-y2 = 1, make a straight line L with an inclination angle of 60 ° and intersect the hyperbola at two points a and B to find | ab|

Through the right focus F of hyperbola x2-y2 = 1, make a straight line L with an inclination angle of 60 ° and intersect the hyperbola at two points a and B to find | ab|

The AB equation is y = tan60 ° X - √ 6,
y=√3x-√6,
And then we put it into hyperbolic equation,
After sorting out: 2x ^ 2-6 √ 2x + 7 = 0,
According to Veda's theorem,
x1+x2=3√2,
x1*x2=7/2,
According to the chord length formula,
|AB|=√(1+k^2)(x1-x2)^2
=√(1+k^2)[(x1+x2)^2-4x1x2]
=√(1+3)(18-4*7/2)
=4.

Elden Ring Premiere

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