Is this a hyperbola? Or maybe a circle? How can you tell? 49x^2-16y^2 = 784?

Question

What is this? How can you tell? I'm personally leaning towards a circle, but I'm not positive...how can I be sure?

Answer 1

Stop leaning, it's a hyperbola! A hyperbola is always the difference of two squared terms. A circle is the sum of two squared terms with equal coefficients.

Answer 2

It's a hyperbola. How do you know? It's easier to say what it's NOT and say why. Well, okay.It is NOT a circle, becaue a circle would have a + sign and the coefficients of x^2 and y^2 would be the same. It's not an ellipse because if it were an ellipse, it would have a plus sign (in an ellipse the x^2 and y^2 coefficients are different.) It's not a parabola, because a parabola only has ONE squared variable. It IS a hyperbola. Out of all the conic sections I just named, it's the only one that makes sense. How do I know? Well, because of the - sign. [[:

Answer 3

This is a hyperbola.
The equation is of the form:
7^2 x^2 - 4^2 y^2 = 28^2
Dividing by 28^2, this becomes:
x^2 / 4^2 - y^2 / 7^2 = 1, matching the standard form for a hyperbola, which is:
x^2 / a^2 - y^2 / b^2 = 1.

For an ellipse, the equation is of the form:
x^2 / a^2 + y^2 / b^2 = 1 ...........(1)

A circle is an ellipse with a and b equal. The equation (1) then becomes:
x^2 + y^2 = a^2.

Answer 4

The - sign tells you it is a hyperbola.

784=49*16, so dividing 49*16, we get
49x^2/49*16 -16y^2/49*16 = 784/49*16
x^/16 - y^2/49 = 1
x^2/4^2 -y^2/7^2 =1
This is clerly an hyperbola.

Answer 5

hyperbola.

circle: 2 positive square terms with equal coefficients
parabola: 1 square term
ellipse: 2 positive square terms with unequal coefficients
hyperbola: 1 positive and 1 negative square term