Ava-May Nelson

2021-02-21

Identify the graph of the given nondegenerate conic sections: ${y}^{2}-12x-4y+52=0$

Malena

Skilled2021-02-22Added 83 answers

Step 1
A nondegenerate conic section of the form
$A{x}^{2}+C{y}^{2}+Dx+Ey+F=0$
a)If $A=C$ then circle
b)If $AC=0$ then the parabola
c)If $A\ne C$ and $AC>0$ then the ellipse
d)If $AC<0$ then hyperbola.
Step 2
Given equation of conics is
${y}^{2}-12x-4y+52=0$
comparing with $A{x}^{2}+C{y}^{2}+Dx+Ey+F=0$ gives
$A=0,C=1,D=-12,E=-4,F=0$
Here $AC=0(1)=0$
Therefore the graph of the given equation is parabola.

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