How do you find the vertices of a hyperbola in standard form?

The hyperbola is centered at the origin, so the vertices serve as the y-intercepts of the graph. To find the vertices, set x=0 x = 0 , and solve for y y . Therefore, the vertices are located at (0,±7) ( 0 , ± 7 ) , and the foci are located at (0,9) ( 0 , 9 ) .

How do you write the standard form of a hyperbola with vertices and foci?

A General Note: Standard Forms of the Equation of a Hyperbola with Center (0,0) Note that the vertices, co-vertices, and foci are related by the equation c2=a2+b2 c 2 = a 2 + b 2 .

How do you find vertices of a hyperbola?

The hyperbola is centered at the origin, so the vertices serve as the y-intercepts of the graph. To find the vertices, set x=0 x = 0 , and solve for y y .

What is the standard form of the equation of a hyperbola?

The standard form of the equation of a hyperbola with center (0,0) ( 0, 0) and transverse axis on the y -axis is Note that the vertices, co-vertices, and foci are related by the equation c2 = a2 +b2 c 2 = a 2 + b 2.

How to find the transverse axis of a hyperbola with Y2 49-x2 32?

Solve for c c using the equation c= √a2 +b2 c = a 2 + b 2. Identify the vertices and foci of the hyperbola with equation y2 49 − x2 32 =1 y 2 49 − x 2 32 = 1. The equation has the form y 2 a 2 − x 2 b 2 = 1 y 2 a 2 − x 2 b 2 = 1, so the transverse axis lies on the y -axis.

What are the conjugate hyperbolas of each other?

2 hyperbolas such that transverse & conjugate axes of one hyperbola are respectively the conjugate & transverse axis of the other are called conjugate hyperbola of each other. (x 2 / a 2) – (y 2 /b 2) = 1 & (−x 2 / a 2) + (y 2 / b 2) = 1 are conjugate hyperbolas of each other.

What is the length of latusrectum of hyperbola?

Lengths of latus-rectum: The length of latus-rectum = (2a 2 / b) = [2 (3) 2] / 4 = 9/2 A circle drawn with centre C & transverse axis as a diameter is called the auxiliary circle of the hyperbola. The auxilary circle of hyperbola equation is given as: