Find the standard form of the equation of the hyperbola with center at the origin, a vertex at (7, 0), and a focus at (10, 0).

A. x^2/9 - y^2/49 = 1
B. y^2/51 - x^2/9 = 1
C. x^2/49 - y^2/51 = 1
D. x^2/9 - y^2/51 = 1

Question

Find the standard form of the equation of the hyperbola with center at the origin, a vertex at (7, 0), and a focus at (10, 0).


A. x^2/9 - y^2/49 = 1
B. y^2/51 - x^2/9 = 1
C. x^2/49 - y^2/51 = 1
D. x^2/9 - y^2/51 = 1

reemii · Answer

draw the two points, can you decide already if it's |dw:1369958086220:dw|
?

reemii · Answer

@rebekita01 ?

anonymous · Answer

idk what it is

reemii · Answer

since it's |dw:1369959000061:dw|
the equation will be $x^2/a^2 - y^2/b^2 = 1$.
use the fact that the point (7,0) is on the hyperbola, and you'll see that $a^2=49$.
only one possibility: option C.