For each of the three equations below determine whether the

For each of the three equations below, determine whether the equation describes a conic section. If an equation does not describe a conic section, state that it is not a conic section, and why. If an equation does describe conic section, put the equation into standard form and identify which type of conic section it is. 5x^2 + 20x + 4y^2 = 40y-100 3/x^2 - x^5 - y^2 - 8 = 0 x^2 = 1

Solution

5x^2 + 20x +4y^2=40y-100

5(x^2+4x) + 4(y^2-10y)=-100

5(x^2+4x+4 -4) + 4(y^2-10y+25-25)=-100

5(x+2)^2 - 20 + 4(y-5)^2 - 100=-100

5(x+2)^2 + 4(y-5)^2=-100+100+20

5(x+2)^2 + 4(y-5)^2=20

(x+2)^2/4 + (y-5)^2/5=1

this equation represents ellipse .

Hence its a conic section

3/x^2   -x^5 -y^2-8=0   This equation doesnot represents any of the conic section (circle,ellipse,parabola,hyperbola). SO it is not representing conic section.

x^2=1   Here the y variable is missing. SO it is not representing conic section