SOLUTION: Write the equation of the hyperbola with a center at (4, -1), transverse axis is parallel to the y-axis, distance between the foci is 10, one endpoint of the conjugate axis is at (

Question 1194738: Write the equation of the hyperbola with a center at (4, -1), transverse axis is parallel to the y-axis, distance between the foci is 10, one endpoint of the conjugate axis is at (6, -1).
Answering this question would mean a lot to me, thanks!!
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
given:
a center at (, ),
transverse axis is parallel to the y-axis,
distance between the foci is ,
one endpoint of the conjugate axis is at (,)

if the transverse axis is parallel to the y-axis, use the standard form

if a center at (, )=> ,

the distance from the center to the given endpoint of the conjugate axis, and we know

so far equation is

The center is its midpoint, so the two foci are (,) and (,).
is distance between center and foci, so
The two blue lines are the latus rectums. They are given as , so by subtraction of half that or from the x-coordinate of the focus (,), we get that
the left end of the upper latus rectum is the point (,

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