SOLUTION: Find the equation of the hyperbola whose centre is (1, 0), one focus is (6, 0) and transverse axis 6.

Question 770449: Find the equation of the hyperbola whose centre is (1, 0), one focus is (6, 0) and transverse axis 6.

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
With the center at (1,0) and a focus 5 units to the right, at (6,0), you know that the focal distance is anf that the transverse axis is along the x-axis.
(You also know that the other focus will be 5 units to the left of the center, at (4,0), and that is useful if you need to sketch the hyperbola).
The equation of a hyperbola with a transverse axis parallel to the x-axis and center at (h,k) is

In this case, since the center is (1,0), the equation is

We need to find and .
is the distance from a vertex to the center, half of the length of the transverse axis.
If the transverse axis is 6, the vertices are 6 units apart,
and they are units from the center.
(If you need to sketch the hyperbola, the vertices are 3 units to the right and 3 units to the left of the center, at (-2,0) and (4,0)).
The other number you need for the equation of the hyperbola is such that
.
So -->-->-->-->
So the equation of the hyperbola in question is
or

RELATED QUESTIONS
Find the equation of the hyperbola which satisfies the given condition . Center (0,0),... (answered by lwsshak3)

Help me to answer this question, please? General Equation and Graph of Hyperbola with: (answered by lwsshak3)

Find the equation of hyperbola, foci at (3,5) and (3,-5), length of transverse axis is... (answered by MathLover1)

find the equation of the hyperbola whose focus is (0,0) and directrix is... (answered by Fombitz)

If foci of a hyperbola are (0,±5) and length of semi transverse axis is 3 units, then... (answered by ikleyn)

Find the equation of hyperbola if transverse axis of hyperbola is along X-axis and its... (answered by CPhill)

If length of transverse axis is 8 and conjugate axis is 10 and transverse axis is along... (answered by ikleyn)

A hyperbola has vertices (±5,0) and one focus at (6,0). What is the equation of the... (answered by MathLover1)

Find the equation (hyperbola) foci at ( - 3, 1) and (7, 1) and length of the... (answered by MathLover1)