Equation of a Hyperbola 1

Multivariable Calculus: Find the center, vertices, foci, and asymptotes of the hyperbola 4x^2 - 16x - y^2 + 6y - 9 = 0. Then sketch the hyperbola.

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[MathDoctorBob]

@pixelated111 If solutions exist, the quick check is to look at the coefficients of x^2 and y^2. If equal, circle. If unequal but same signs, ellipse. If unequal signs, hyperbola.

Here the coefficients have opposite signs, so hyperbola. The general equation of a hyperbola is either x^2/a^2 - y^2/b^2 = 1 or y^2/a^2 - x^2/b^2 = 1. - Bob