Identify the following conic. That is, is it circle, parabola, hyperbola, or ellipse? Show why.
x^2 - 4y^2 - 4x - 24y = 48
2007-07-08 19:41:42 · 2 answers · asked by Sara 3 in Science & Mathematics ➔ Mathematics
The general equation of a quadratic is:
ax² + bxy + cy² + dx + ey + f = 0
The discriminant b² - 4ac = 0 - 4*1*(-4) = 16 > 0
Since the discriminant is greater than zero it is a hyperbola.
2007-07-08 19:52:29 · answer #1 · answered by Northstar 7 · 0⤊ 0⤋
The words x^2 and y^2 are the two efficient. this exhibits it is the two a circle or an ellipse (or probable a ingredient or the empty set). The coefficients of x^2 and y^2 are the two a million. this exhibits it is a circle (or probable a "degenerate circle - radius 0 or the empty set) To get the radius, shall we desire to end the sq. upload a million+9 to the two factors to end the sq. for x and y. The equation (x-a million)^2 + (y-3)^2 = 36 it is a circle with middle (a million,3) and radius ?36 = 6.
2016-12-10 06:20:35 · answer #2 · answered by ? 4 · 0⤊ 0⤋