Precalculus 2014
82

 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 .

TESTIMONIALS
 "I want to tell you that our students did well on the math exam and showed a marked improvement that, in my estimation, reflected the professional development the faculty received from you. THANK YOU!!!" June Barnett "Your site is amazing! It helped me get through Algebra." Charles "My daughter uses it to supplement her Algebra 1 school work. She finds it very helpful." Dan Pease
 Tweets by @mathskeydotcom

QUESTIONS? LET US HELP.