Respuesta :
Answer:
16x^2 - 49y^2 = 784
Step-by-step explanation:
as we know that this is the standard equation of hyperbola bcz 1 coordinate of vertices is 0.
since in vertices x coordinate is present and y coordinate is 0 so Tranverse axis of hyperbola is along x axis .
vertices in general = (a,0) and (-a,0)
vertices given = ( 7,0) and (-7 , 0)
so a=7
similarly
co vertices in general = ( 0 , b) and ( 0 , -b)
co vertices given = ( 0, 4) and (0 , -4)
so,
b= 4
now equation for x axis is:
(x2/a2) - ( y2/b2) = 1
by putting values we observe the ans is
16x^2 - 49y^2 = 784
Answer:
[tex]\frac{x^{2} }{49}-\frac{y^{2} }{16}=1[/tex] is the equation of hyperbola.
Step-by-step explanation:
Given:
Vertices of the hyperbola: (-7,0) and (7,0)
Co-vertices of the hyperbola: (0,-4) and (0,4)
Mid-point of the vertices = center of hyperbola = (0,0)
Focii lie on the same line as vertices and hence they lie on x-axis.
Here x-axis is the tranverse axis and y-axis is the conjugate axis.
length of semi-transverse axis = a = 7
length of semi-conjugate axis = b = 4
Equation of hyperbola is of the form:
[tex]\frac{x^{2} }{a^{2} }-\frac{y^{2} }{b^{2} }=1[/tex]
Substituting a = 7 and b = 4 we get:
[tex]\frac{x^{2} }{49}-\frac{y^{2} }{16}=1[/tex]
[tex]16x^{2} -49y^{2}=784[/tex]
