Match the equation with its graph. GRAPH CAN'T COPY....

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Key Concepts

Asymptotes

Asymptotes are straight lines that guide the behavior of a hyperbola at extreme values of x and y. For a horizontal hyperbola in standard form, the asymptotes have equations y = ±(b/a)x. They serve as a framework for graphing the hyperbola accurately by providing the directional limits toward which the branches of the hyperbola approach.

Conic Sections

Conic sections are curves obtained by intersecting a plane with a double-napped cone. This includes circles, ellipses, parabolas, and hyperbolas. Understanding their general definitions and properties is key to identifying and graphing the corresponding equations.

Hyperbola

A hyperbola is a type of conic section characterized by two separate branches. It is defined as the set of points where the difference of the distances to two fixed points (the foci) is constant. The shape and orientation of a hyperbola depend on the standard equation and its coefficients.

Standard Form of a Hyperbola

The standard form for a horizontal hyperbola is given by (x²/a²) - (y²/b²) = 1, where a and b are real numbers that determine the distances from the center to the vertices and the slope of the asymptotes respectively. This form is crucial for identifying key features such as the center, vertices, and asymptotes.

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