Find the standard form of the equation of the hyperbola with the given characteristics. Vertices: (4, -1), (4, -7); Asymptotes: y = x - 8, y = -x
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
It is given that the vertices are and .
The asymptotes are and .
Here, the vertices are have the same x coordinate. Therefore, the hyperbola has a vertical transverse axis.
Thus, the standard form of the hyperbola is .
Now find the value of h, k and a using the vertices.
The vertices of the hyperbola are of the form .
Here, and .
That is, and .
Thus, the value of k is obtained as follows.
Also,
Therefore, the value of a is 3.
Thus, the values are .
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