Question

What is the nature of the graph : $y=-4x^2+6$

• A. parabola not passing through origin
• B. Hyperbola not passing through origin
• C. Ellipse not passing through origin
• D. it is not a conic

Answer 1

Answer: (A)

parabola not passing through origin

$y=-4x^2+6$

$y-6=-4x^2$
$x^2=\frac{-(y-6)}{4}$

$\to X^2=-4aY$

Where $a=\frac{1}{16}$ and $Y=y-6$.

Hence the above equation is of a parabola not passing through origin.