Tofind:the equation of the hyperbola in which the vertices of the hyperbola is equal to the fociof this ellipse.
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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