Question

Which conic section does the equation below describe? (x - 3)^2)/10 - (y + 5)^2)/9 = 4

Answer 1

The given equation is of the form:

((x - h)^2)/a^2 - ((y - k)^2)/b^2 = 1

Comparing it with the given equation:

((x - 3)^2)/10 - ((y + 5)^2)/9 = 4

We can rewrite the equation in the standard form by dividing both sides by 4, then adding (y+5)^2/9 to both sides:

((x - 3)^2)/40 - ((y + 5)^2)/36 = 1

Now, we can see that the equation is in the standard form of a hyperbola. The center of the hyperbola is (3, -5), the distance between the center and each vertex is sqrt(10) in the x-direction and sqrt(9) in the y-direction, and the hyperbola opens to the left and right.