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Tofind:the equation of the hyperbola in which the vertices of the hyperbola is equal to the fociof this ellipse.
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Answer to Problem 73RE
The equation of hyperbola is
Explanation of Solution
Given:
Vertices of the hyperbola is equal to the foci of the ellipse.
Concept used:
Formula for ellipse:
The point
The coordinates of the vertices are
The coordinates of the foci are
Formula for hyperbola forming open left and right:
Center=
Vertices=
Calculation:
According to the given equation:
The equation is of ellipse.
Vertices=
Foci=
Foci=
So, vertices of hyperbola=
Foci of hyperbola=
Let equation of hyperbola:
Vertices of ellipse=
So,
So, equation of hyperbola is
Hence, the equation of hyperbola is
Chapter 10 Solutions
Precalculus
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