Question

The center of a hyperbola is (−2,4) , and one vertex is (−2,7) . The slope of one of the asymptotes is 1/2 .

Answer 1

The equation of the hyperbola in standard form is (y^2 / 49) - (x^2 / 4) = 1.

Step-by-step explanation:

1. Hyperbola is a section of the cone formed by intersecting a right circular cone with a plane at an angle where both halves of the cone are intersected.
2. The vertex and the center of the hyperbola are present both on the same line x = -2. (i.e. on the y-axis), hence the branches of the hyperbola are above and below each other. The slope of the asymptotes is +(or)- a/b.

Here the vertex is 7 units so a = 7 and a^2 = 49.

Slope of the asymptotes = a/b = 1/2.

Here b = 2 and b^2 = 4.

The standard equation of the hyperbola is,

                                  (y^2 / 49) - (x^2 / 4) = 1.