math question?

Question

does anyone know the answer to this question?

x squared - y squared = 10

the answer is either a. a circle b. an ellipse c. a hyperbola or d. a parabola

Answer 1

x^2 - y^2 = 10 is the equation for a circle.

You should memorize the general formulas for the different conic sections:

The circle whose center is (x1, y1) and radius is r, is:
(x - x1)^2 + (y - y1)^2 = r^2

The general equation for an ellipse is
[(x - x1)^2]/a^2 + [(y - y1)^2]/b^2 = 1

(note that if a = b = r, you just get a circle, which is why we sometimes say a circle is a special case of an ellipse)

A hyperbola is just the same, only with a minus in the middle
[(x - x1)^2]/a^2 - [(y - y1)^2]/b^2 = 1

And a parabola will only have ONE of the variables squared, either x or y but not both.

Answer 2

Well, the answers seem to be pointing you to a wrong direction. The correct answer is C. a hyperbola.

In a general conic equation,

Ax^2 + Cy^2 + Dx + Ey + F = 0 (B is intendedly left out because it is supposed to be the coefficient of xy) if

A = C, then it is a circle (exactly the same, number and sign)
A or C = 0 (but not both), then it is a parabola
A <> (not equal to) C, and if their signs are the same, then it is an ellipse.
A <> C, and different signs, then it is a hyperbola.

Since x^2 - y^2 - 10 = 0 has A = 1, and B = -1, then it should be a hyperbola.

Hope that helps!!!

Answer 3

If you have x² - y² = 10 then it is a Hyperbola.

This is because:
1.) one is a positive and the other is a negative. (+x² and -y²)
and

If they were both positive it would be a circle.
If they were both positive, but with different constants, it would be an eclipse.
(A circle is always an eclipse, but an eclipse is only a circle when the x and y are scaled the same)

Answer 4

try - when y = 0, x = + or - r sq root of 10

when x = 0, y = + or - sq root of - 10 - imaginary numbers

so the line crosses on the x-axis the origin either side but not at all on the y-axis

not a or b then

c it is

http://en.wikipedia.org/wiki/Hyperbola

Answer 5

x^2 - y^2 = 10

this is the equation of a hyperbola, so c) is the answer

Answer 6

this will be a circle becuase the coefficients and exponents are the same. The radius of he circle will be the square root of ten.