0
Use this as an example:
9x2-16y2+18x+160y-247=0
First put the equation into standard form.
9x² - 16y² + 18x + 160y - 247 = 0
Now complete the square.
9(x² + 2x + 1) - 16(y² - 10y + 25) = 247 + 9 - 400
9(x + 1)² - 16(y - 5)² = -144
Multiply thru by -1 since the right hand side is negative.
16(y - 5)² - 9(x + 1)² = 144
Set equal to one.
(y - 5)²/9 - (x + 1)²/16 = 1
Since y² is the positive squared term, the pair of hyperbolas open vertically up and down.
The center (h,k) = (-1,5).
a² = 9 and b² = 16
a = 3 and b = 4
The vertices are (h,k-a) and (h,k+a) or
(-1,5-3) and (-1,5+3) which is (-1,2) and (-1,8).
c² = a² + b² = 9 + 16 = 25
c = 5
The foci are (h,k-c) and (h,k+c) or
(-1,5-5) and (-1,5+5) which is (-1,0) and (-1,10).
What else can I help you with?
The transverse axis connects what?
The transverse axis is a connection on a hyperbola. It connects the focus, or center, of the hyperbola, and can connect two together.
What is an eccentric circle?
For Ellipse: The 2 circles made using the the ellipse center as their center, and major and minor axis of the ellipse as the dia.For Hyperbola: 2 Circles with centers at the center of symmetry of the hyperbola and dia as the transverse and conjugate axes of the hyperbolaRead more: eccentric-circles
Does a hyperbola have coverticies?
Yes, a hyperbola has co-vertices, but they are not as commonly referenced as in ellipses. The co-vertices of a hyperbola are points that lie along the transverse axis and are used to define the shape of the hyperbola. Specifically, for a hyperbola centered at the origin with a horizontal transverse axis, the co-vertices are located at ((0, \pm b)), where (b) is the distance from the center to the co-vertices. However, these points do not play a significant role in the hyperbola's properties compared to the vertices and foci.
How many lines of symmetry does a hyperbola have?
A hyperbola has two lines of symmetry. These lines of symmetry are the axes that pass through the center of the hyperbola: one is the transverse axis, which runs between the two branches, and the other is the conjugate axis, which is perpendicular to the transverse axis.
What expression gives the length of the transverse axis of a hyperbola?
The length of the transverse axis of a hyperbola is given by the expression (2a), where (a) is the distance from the center of the hyperbola to each vertex. In standard form, the equation of a hyperbola can be represented as (\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1) for a horizontally oriented hyperbola, or (\frac{(y-k)^2}{a^2} - \frac{(x-h)^2}{b^2} = 1) for a vertically oriented hyperbola. In both cases, (a) determines the length of the transverse axis.
What is the term of two lines crossing the center of a graph if its a hyperbola?
The axes of the hyperbola.
What are the followings-hyberbola-asymptotes of hyperbola-centre of hyperbola-conjugated diameter of hyperbola-diameter of hyperbola-directrices of hyperbola-eccentricity of hyperbola?
Asymptotes are the guidelines that a hyperbola follows. They form an X and the hyperbola always gets closer to them but never touches them. If the transverse axis of your hyperbola is horizontal, the slopes of your asymptotes are + or - b/a. If the transverse axis is vertical, the slopes are + or - a/b. The center of a hyperbola is (h,k). I don't know what the rest of your questions are, though.
The transverse axis connects what?
The transverse axis is a connection on a hyperbola. It connects the focus, or center, of the hyperbola, and can connect two together.
What is the hyperbola's point halfway between its two vertices?
Center
What is the point halfway between its two vertices?
The center of a hyperbola is the point halfway between its foci. A hyperbola is defined as 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.
What is the length of letus rectum of hyperbola?
The length of the latus rectum of a hyperbola is given by the formula ( \frac{2b^2}{a} ), where ( a ) is the distance from the center to the vertices and ( b ) is the distance from the center to the co-vertices. This length represents the width of the hyperbola at the points where it intersects the corresponding directrices. For hyperbolas oriented along the x-axis or y-axis, this formula applies similarly, with the values of ( a ) and ( b ) depending on the specific equation of the hyperbola.
What is an eccentric circle?
For Ellipse: The 2 circles made using the the ellipse center as their center, and major and minor axis of the ellipse as the dia.For Hyperbola: 2 Circles with centers at the center of symmetry of the hyperbola and dia as the transverse and conjugate axes of the hyperbolaRead more: eccentric-circles
Does a hyperbola have coverticies?
Yes, a hyperbola has co-vertices, but they are not as commonly referenced as in ellipses. The co-vertices of a hyperbola are points that lie along the transverse axis and are used to define the shape of the hyperbola. Specifically, for a hyperbola centered at the origin with a horizontal transverse axis, the co-vertices are located at ((0, \pm b)), where (b) is the distance from the center to the co-vertices. However, these points do not play a significant role in the hyperbola's properties compared to the vertices and foci.
How many lines of symmetry does a hyperbola have?
A hyperbola has two lines of symmetry. These lines of symmetry are the axes that pass through the center of the hyperbola: one is the transverse axis, which runs between the two branches, and the other is the conjugate axis, which is perpendicular to the transverse axis.
Does a conic section have vertices?
No, a conic section does not have vertices. If it is a circle, it has a center; if it is a parabola or hyperbola, it has a focus; and if it is an ellipse, it has foci.
What do you say about the eccentricity e of a hyperbola?
A hyperbola is a math term meaning a curve in which the distances form either a fixed point or a straight line with a fixed ratio. The formula to find the eccentricity of a hyperbola is "E=C/A," with A being the distance from the center to the focus, and C being the distance from the center to the vertex. Math fans say that solving this formula is about as easy as solving for the area of a triangle, meaning it is not a difficult concept to master.
Which expression gives the length of the transverse axis of the hyperbola shown below?
a - b
