The equation of the hyperbola that has a center at ( 6 , 9 ) , a focus at ( 11 , 9 ) , and a vertex at ( 9 , 9 ) (x−C)^2/A^2−(y−D)^2/B^2=1

Question

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Respuesta :

okpalawalter8 okpalawalter8 · Answer 1 · 2021-05-10T03:34:13+02:00

Answer:

[tex]A=-3[/tex]

[tex]C=6[/tex]

[tex]B=4[/tex]

[tex]D=9[/tex]

Step-by-step explanation:

From the question we are told that:

Center of hyperbola at ( 6 , 9 )

Focus of hyperbola at ( 11 , 9 )

Vertex of hyperbola at ( 9 , 9)

Equation of hyperbola [tex]\frac{(x-C)^2}{A^2} -\frac{(y-D)^2}{B^2}=1[/tex]

Generally the C and D of the hyperbola equation is mathematically given by

[tex]Centers (6,9)[/tex]

[tex]C=6[/tex]

[tex]D=9[/tex]

Generally the A and B a of the hyperbola equation is mathematically given by

[tex]A=x_c-x_v[/tex]

[tex]A=6-9[/tex]

[tex]A=-3[/tex]

[tex]C'=x_c-x_f[/tex]

[tex]C'=6-11[/tex]

[tex]C'=-5[/tex]

Therefore with Center,Focus ,Vertex on the same line

[tex]B^2=C'^2-A^2[/tex]

[tex]B^2=(-5^2)-(-3^2)^2[/tex]

[tex]B^2=(25)-(9)[/tex]

[tex]B^2=16[/tex]

[tex]B=4[/tex]