How do you determine circle, parabola, ellipse, or hyperbola from equation $4 x^{2} - 9 y^{2} - 16 x + 18 y - 11 = 0$ $4x^2 - 9y^2 - 16x +18y -11 = 0$ ?

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Answer 1 · 2015-11-12T00:44:30

EVERY conic section can be written with the general equation :

$A x^{2} + B y^{2} + C x + D y + E = 0$ $Ax^2+By^2+Cx+Dy+E=0$

Here is how you distinguish the various conic sections from the coefficients in the general equation:

circle : $A = B$ $A=B$

ellipse : $A \neq B$ $AneB$ but A and B both have the SAME sign (+ or -)

hyperbola : $A \neq B$ $AneB$ but A and B both have DIFFERENT signs

parabola : either A or B equals 0 (only one squared term in the equation)

So, in the problem stated above, since $A \neq B$ $AneB$ ( $4 \neq 9$ $4ne9$ ), but A and B have different signs (4 and -9), it is a hypebola !

hope that helped

How do you determine circle, parabola, ellipse, or hyperbola from equation 4x2−9y2−16x+18y−11=04x^2 - 9y^2 - 16x +18y -11 = 0?