Answer
A - Hyperbola
B - Ellipse ( More accurately a circle, in this case)
C - Ellipse
D - Hyperbola
E - Ellipse
F - Ellipse (More accurately a circle, in this case)
G - Hyperbola
H - Ellipse
Work Step by Step
Standered Form of a:
Ellipse:
$\frac{x^{2}}{a^{2}}$ + $\frac{y^{2}}{b^{2}}$ = 1
Hyperbola
$\frac{x^{2}}{a^{2}}$ - $\frac{y^{2}}{b^{2}}$ = 1
Now,
Comparing A-H with the above two equations,
We have:
A - Hyperbola - Notice the minus sign in the equation.
B - Ellipse - Notice the plus sign in the equation.
Notice that the values of a and b are equal ($a^{2}=b^{2}$), and hence the given ellipse is a more accurately a circle. Answer: ellipse isn't wrong, the more accurate answer is a circle.
C - Ellipse - Notice the plus sign in the equation.
D - Hyperbola - Notice the minus sign in the equation.
E - Ellipse - Notice the plus sign in the equation.
F - Ellipse - Notice the plus sign in the equation.
Notice that the values of a and b are equal ($a^{2}=b^{2}$), and hence the given ellipse is a more accurately a circle. Answer: ellipse isn't wrong, the more accurate answer is a circle.
G - Hyperbola - Notice the minus sign in the equation.
H - Ellipse - Notice the plus sign in the equation.
