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The fifth problem of hyperbola in high school mathematics
A straight line intersects the right branch of a hyperbola at different points. Note that the right branch of the hyperbola has two different intersections. X > in hyperbola; 0 linear equation and hyperbolic equation are simultaneous,

X squared -(kx+2) squared = 6(x >;; 0)

Finishing, (1-k squared) x squared-4kx-10 = 0 (x >); 0)

Intersecting at two different points, that is, this formula has two unequal positive real roots,

Discriminant δ= 16k square +40( 1-k square) =40-24k square > 0.

That is, k party.

Find the root 15/3

The above only satisfies that a straight line and a hyperbola have two different intersections, regardless of the left and right branches.

If the intersection with the right branch is limited, the following conditions must be met at the same time

x 1x 2 & gt; 0x 1+x2 & gt; 0

now

4k/ 1-k squared > 0-10/ 1-k >: 0

Solution {0

To sum up, the value range of k is-root15/3 < k <; - 1

Answer d