Answer to Question #226831 in Analytic Geometry for Chhes

Question

Direction: Tell whether the equation represents a circle, parabola, ellipse or hyperbola.

1. 3x^2+6x-5y-7=0

Answer 1

3x²+6x-5y-7=0

5y=3x²+6x-7

y=0.6x²+1.2x-1.4

The equation cuts line x=0 at -1.4 and cuts line y=0 at -0.4 and +1.6

The parabolic equation cuts either y or x axis once and the corresponding x or y axis twice. Therefore, since the above equation obeys the definition of a parabolic equation, then the equation is a parabola.