# Recognize the equation and important characteristics of the different types of conic sections, illustrate systems of nonlinear equations, determine the solutions of system of equations (one linear and one second degree) in two variables using substitution, elimination, and graphing (in standard form), solve situational problems involving systems of non-linear equation Write the following equation in standard form and sketch it's graph 1.9x^2+72x-64y^2+128y+80=0 2.y^2+56x-18y+417=0 3.x^2-10x-48y+265=0 4.x^2+4x+16y^2-128y+292=0

Question
Forms of linear equations
Recognize the equation and important characteristics of the different types of conic sections, illustrate systems of nonlinear equations, determine the solutions of system of equations (one linear and one second degree) in two variables using substitution, elimination, and graphing (in standard form), solve situational problems involving systems of non-linear equation
Write the following equation in standard form and sketch it's graph
1.$$9x^2+72x-64y^2+128y+80=0$$
2.$$y^2+56x-18y+417=0$$
3.$$x^2-10x-48y+265=0$$
4.$$x^2+4x+16y^2-128y+292=0$$

2021-01-08
Given equation is $$9x2+72x−64y2+128y+80=0$$.
Given equation can be written as:
$$9x^2+72x−64y^2+128y+80=0$$
$$(3x)^2+2*3x*12+(12)^2−144−[64y^2−128y]+80=0$$
$$(3x+12)^2−(64y^2−128^y+64−64)+80−144=0$$
$$(3x+12)^2−(8y−8)^2=0$$
Given equation is pair of straight lines.

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$$\displaystyle{f{{\left({f{{\left({x}\right)}}}\right)}}}={9}{x}-{8}$$
$$\displaystyle{f{{\left({f{{\left({x}\right)}}}\right)}}}={x}^{{{4}}}-{12}{x}^{{{2}}}+{30}$$