Several solutions to a system of linear equations with three variables

There are three unknowns, and the degree of each term with unknowns is once. Generally speaking, there are three equations (sometimes there are special cases, but all the ternary linear equations have three unknowns). Such equations are called ternary linear equations

Solution of ternary linear equations

The solution of ternary linear equations is similar to that of binary linear equations
Method 1: one equation is transformed into another two equations to get a system of quadratic equations
Method 2: a binary system of linear equations was obtained by adding and subtracting the ternary system of linear equations

To find the standard hyperbolic equation suitable for the following conditions, it is necessary to solve the problem
1. The focus is on the x-axis, the real axis length is 10, and the imaginary axis length is 8;
2. The focus is on the y-axis, the focal length is 10, and the imaginary axis length is 8

1, let the equation be x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1, from the title: real axis 2A = 10, imaginary axis 2B = 8, so: a = 5, B = 4; so the equation is x ^ 2 / 25-y ^ 2 / 16 = 12, let the equation be y ^ 2 / A ^ 2-x ^ 2 / b ^ 2 = 1, from the title: focal length 2C = 10, imaginary axis 2B = 8, so: B = 4, C = 5, a ^ 2 = C ^ 2-B ^ 2 = 25-16 = 9, so the equation

What is the standard equation of hyperbola

Hyperbola has two collimators L1 (left collimator), L2 (right collimator) the equation of the hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 is x = a ^ 2 / C (denoted as a part of C), the equation of the hyperbola y ^ 2 / A ^ 2-x ^ 2 / b ^ 2 = 1 is y = a ^ 2 / C, where a is the real half axis length, B is the imaginary half axis length, and C is the half focal length

Several solutions to a system of linear equations with three variables