SOLUTION: Find the standard form of the equation of the hyperbola satisfying the given conditions. ​x-intercepts (0,24) and (0,-24). foci at (-26,0) and (26,0) The equation in standa

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the standard form of the equation of the hyperbola satisfying the given conditions. ​x-intercepts (0,24) and (0,-24). foci at (-26,0) and (26,0) The equation in standa      Log On


   



Question 1149989: Find the standard form of the equation of the hyperbola satisfying the given conditions.
​x-intercepts (0,24) and (0,-24). foci at (-26,0) and (26,0)
The equation in standard form of the hyperbola is..

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given:
the hyperbola satisfying the given conditions
​x-intercepts (0,24) and (0,-24) =>wrong, these are y-intercepts
the hyperbola has a vertical transverse axis and its standard form of the equation is:
%28y-k%29%5E2%2Fa%5E2-%28x-h%29%5E2%2Fb%5E2=1
foci at (-26,0) and (26,0)=>The center lies on the x-axis and center is at (0,0)
then, your formula is y%5E2%2Fa%5E2-x%5E2%2Fb%5E2=1

The distance from the center point to one focus is called c and can be found using this formula:
c%5E2+=+a%5E2+%2B+b%5E2=> since c=26
a%5E2+%2B+b%5E2=26%5E2
a%5E2+=26%5E2-b%5E2


use y-intercept (0,24) and a%5E2+=26%5E2-b%5E2, plug in
y%5E2%2Fa%5E2-x%5E2%2Fb%5E2=1

24%5E2%2F%2826%5E2-b%5E2%29-0%5E2%2Fb%5E2=1.......solve for b
24%5E2%2F%2826%5E2-b%5E2%29=1
24%5E2=26%5E2-b%5E2
b%5E2=26%5E2-24%5E2
b%5E2=100
b=10
find a:
a%5E2+=26%5E2-10%5E2
a%5E2+=576
and, your formula is: y%5E2%2F576-x%5E2%2F100=1