0
The standard form of a hyperbola in an x-y plot is (x-m)2/a2 - (y-n)2/b2 = +/- 1 (meaning either + or -), where (m,n) is the point of symmetry.
Let us take the case of +1 on the right-hand side.
Expanding the equation, we have
b2x2 - x * (2mb2) - a2y2 + y * (2na2) = a2b2 - b2m2 + a2n2
You have to match the coefficients of your equation to the ones above.
Let us assume your equation is x2 - y2 = 1, which will be trivial to do.
Matching the coefficients, you have m = 0 = n and a = +/-1 = b (insufficient information to determine + or -).
Another simple example for your equation: 9x2 - 18x - 4y2 - 8y = 31.
Matching coefficients exactly, we have
b2 = 9 -- (1)
-2mb2 = -18 -- (2)
-a2 = -4 -- (3)
2na2 = -8; and -- (4)
a2b2 - b2m2 + a2n2 = 31 -- (5)
(1) is simplified to b = +/-3 (no way knowing + or -)
(3) is simplified to a = +/-2
(1) substituted into (2), (2) becomes m = 1
(3) substituted into (4), (4) becomes n = -1
Substituting (1-4) into 5, we have the LHS = 36 - 9 + 4 = 31 = RHS.
For our convenience, if +/- cannot be determined, take the + for the equation coefficients. Hence, a = 2 and b = 3.
Q.E.D.
What else can I help you with?
The vertex form of the equation of a parabola is y x-5 2 plus 16 what is the standard form of the equation?
In the equation y x-5 2 plus 16 the standard form of the equation is 13. You find the answer to this by finding the value of X.
How do you convert an equation in standard form to slope-intercept form?
Solve the equation for ' y '.
How do you find the standard form of a linear equation knowing only the y intercept and the slope IE A line has a slope of 5 over 3 and a y intercept of 1 over 2 State the equation in standard form?
Since we know the slope, m = 5/3, and the y-intercept 1/2, we arw able to write the equation of the line in the slope-intercept form, y = mx + b, so we have y = (5/3)x + 1/2.The standard form of the equation of the line is Ax + By = C.y = (5/3)x + 1/2y - y - 1/2 = (5/3)x - y + 1/2 - 1/2-1/2 = (5/3)x - y or(5/3)x - y = -1/2Thus, the standard form, Ax + By = C, of the equation of the line is (5/3)x - y = -1/2.
What different information do you get from vertex form and quadratic equation in standard form?
The graph of a quadratic function is always a parabola. If you put the equation (or function) into vertex form, you can read off the coordinates of the vertex, and you know the shape and orientation (up/down) of the parabola.
How do you find the vertex from a quadratic equation in standard form?
look for the interceptions add these and divide it by 2 (that's the x vertex) for the yvertex you just have to fill in the x(vertex) however you can also use the formula -(b/2a)
What does each variable represent in standard form?
There are different standard forms for different things. There is a standard form for scientific notation. There is a standard form for the equation of a line, circle, ellipse, hyperbola and so on.
Which equation below represents a generic equation suggested by a graph showing a hyperbola?
A hyperbola is another form of a conical section graph like a parabola or ellipse. Its general form is x^2/a - y^2/b = 1.
How do you write the equation for each hyperbola in standard form when the equation is y2-3x2 plus 6x plus 6y equals 18?
y2-3x2+6x+6y= 18 is in standard form. The vertex form would be (y+3)2/24 - (x-1)2/8 = 1
The vertex form of the equation of a parabola is y x-5 2 plus 16 what is the standard form of the equation?
In the equation y x-5 2 plus 16 the standard form of the equation is 13. You find the answer to this by finding the value of X.
What is standard form linear equation's?
A standard form of a linear equation would be: ax + by = c
How do you find the slope and y-intercept for y equals 2x-3?
5
How do you find the x and y intercepts of a linear equation in standard form?
The y-intercept is c in the standard form. The x-intercept is -c/m.
What is the standard form of an equation?
The standard form of an equation is Ax + By = C. In this type of equation, x and y are variables while A, B, and C are integers.
How do you convert an equation in standard form to slope-intercept form?
Solve the equation for ' y '.
How do you convert standard form to factored form?
To convert a quadratic equation from standard form (ax^2 + bx + c) to factored form, you first need to find the roots of the equation by using the quadratic formula or factoring techniques. Once you have the roots, you can rewrite the equation as a product of linear factors, such as (x - r1)(x - r2), where r1 and r2 are the roots of the equation. This process allows you to express the quadratic equation in factored form, which can be useful for solving and graphing the equation.
Find an equation in standard form for the passing through the points 1 4 and -3 4?
6666
How do you find the center and radius with an equation not in standard form?
By using Cartesian equations for circles on the Cartesian plane
