Question

Which of the following equations would produce a parabola? Check all that apply. –5x2 4x – 7y 14 = 0 –x2 6x y2 – 8 = 0 9x2 – 12xy 4y2 4x – y 5 = 0 12x 6y – 5y2 14 = 0 20x2 10xy – y2 3x – 6y 5 = 0.

Answer 1

Equations 1 and 4 would produce a parabola as they follow the general equation of a parabola.

Given equations are:

$1)-5x^2+4x-7y+14 = 0\\\\2)-x^2 + 6x +y^2-8=0\\\\3)9x^2-12xy+4y^2+4x-y+5=0\\\\4)12x+6y-5y^2+14=0$

What is the general equation of a parabola?

The general equation of a parabola

$y = a(x^2+h^2-2xh)+k$ or $x= a(y^2+k^2-2yk)+h$

where h and k are vertices of the parabola.

Each equation follows the same pattern as the general equation of a parabola except the second and third equation

Therefore, equations 1 and 4 would produce a parabola as they follow the general equation of a parabola.

To get more about parabola visit:

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