How do you write an equation for the hyperbola with center at (-2,-3), Focus at (-4,-3), Vertex at (-3,-3)?

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Answer 1 · 2016-02-13T09:37:25

Equation of hyperbola is #(x+2)^2/1-(y+3)^2/3=1#

As #y# coordinates of center, focus, and vertex all are #-3#, they lie on the horizontal line #y =-3# and general form of such hyperbola is

#(x-h)^2/a^2-(y-k)^2/b^2=1#, where#(h,k)# is center.

Here center is #(-2,-3)#.

Further, #a# is distance of vertex from center and #a^2+b^2=c^2#, where #c# is distance of focus from center.

As the vertex is 1 units from the center, so #a = 1#; the focus is 2 units from the center, so #c = 2#.

As #a^2+b^2=c^2#, #b^2=c^2-a^2=4-1=3#.

Equation of hyperbola is hence

#(x+2)^2/1-(y+3)^2/3=1#