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.
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.
Solve the equation for ' y '.
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.
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.
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)
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.
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.
y2-3x2+6x+6y= 18 is in standard form. The vertex form would be (y+3)2/24 - (x-1)2/8 = 1
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.
A standard form of a linear equation would be: ax + by = c
5
The y-intercept is c in the standard form. The x-intercept is -c/m.
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.
Solve the equation for ' y '.
By using Cartesian equations for circles on the Cartesian plane
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ax+by=c