Question 759156
Find the standard form of the equation of the hyperbola with the given characteristics and center at the origin.
Vertices: (±1, 0); asymptotes: y = ±7x
***
Given hyperbola has a horizontal transverse axis as noted from given coordinates of vertices:
Standard form of equation: {{{(x-h)^2/a^2-(y-k)^2/b^2=1}}},(h,k)=(x,y) coordinates of center
Given center:(0,0)
a=1(distance from center to vertices)
a^2=1
..
slope of asymptotes=±7
slopes of asymptotes of hyperbolas with horizontal transverse axis=b/a=±7
b=±7a
b=49a^2=49
Standard form of equation of the hyperbola: {{{x^2-y^2/49=1}}}