The centre, vertices, foci, and the equations of the asymptotes of the hyperbola using sketch.
Answer to Problem 38RE
Centre
Vertices
Foci
Equation of the hyperbola
Explanation of Solution
Given information:
The centre, vertices, foci, and the equations of the asymptotes of the hyperbola.
Calculation:
The asymptotes is given by:
By completing the square,
Divide the equation by
The equation is in the standard form of a hyperbola with vertical transverse axis:
Where
Now, find the vertices of the hyperbola of the equation:
By using the relationship
The vertices are
The foci are
The equation for the asymptotes when the transverse axis is vertical is:
The graph will be:
Thus, the centre, vertices, foci, and the equations of the asymptotes of the hyperbolaare
Chapter 10 Solutions
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