Which is the equation of a hyperbola centered at the origin with focus (-3,0) and vertex (-2,0)

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08-09-2022
Mathematics

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Which is the equation of a hyperbola centered at the origin with focus (-3,0) and vertex (-2,0)

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rafikiedu15 rafikiedu15 · Answer 1 · 2022-09-22T14:23:42+02:00

Main answer:[tex]x^{2}[/tex]/4 - [tex]y^{2}[/tex]/5=1

Definition of Hyperbola=a symmetrical open curve formed by the intersection of a circular cone with a plane at a smaller angle with its axis than the side of the cone.

Formula=[tex](x-x1)^{2}[/tex]/[tex]a^{2}[/tex] - [tex](y-y1)^{2}[/tex]/[tex]b^{2}[/tex]=1

Given,

origin o(0,0) , focus s(-3,0) , vertex v(-2,0)

and , x1=0, y1=0

then, equation of hyperbola becomes= [tex]x^{2}[/tex]/[tex]a^{2}[/tex]-[tex]y^{2}[/tex]/[tex]b^{2}[/tex]=1

a is the distance between center and the vertex,

distance between o and v = 2

c is the distance between center and the focus,

distance between o and s =3

[tex]a^{2}[/tex]+[tex]b^{2}[/tex]=[tex]c^{2}[/tex]

4+[tex]b^{2}[/tex]=9

[tex]b^{2}[/tex]=5

Then the equation of hyperbola becomes=[tex]x^{2}[/tex]/4 -[tex]y{2}[/tex]/5=1

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