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| PAGE: 579 | SET: Exercises | PROBLEM: 82 |
The equation is 
.
Rewrite the above equation 
.
Compare the above equation with polar equation of conic 
.
Here 
and 
.
Since 
, the equation is hyperbola.
The directrix of the hyperbola is 
.
The general equation of hyperbola in rectangular form : 
.
The vertices lie on the transverse axis.
The vertices occur when 
and 
.
Case 1 : When 
.
Substitute in the above equation.
Case 2 : When 
.
Substitute in the above equation.
The polar coordinates of the vertices are 
and 
correspond to the rectangular coordinates are and 
.
The hyperbola’s center is the midpoint of the vertices 
.
The distance between the center and each vertex is 
.
The distance from the center 
to the focus at 
is 
.
Substitute corresponding values in the general equation of hyperbola.
Substitute corresponding values in 
.
The equation of hyperbola is 
.
The equation of hyperbola is 
.
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