(a)Use the discriminant to determine whether the graph of the following equation is a parabola, an ellipse, or a hyperbola:
(b) Use rotation of axes to eliminate the -term in the equation.
(c) Sketch a graph of the equation.
(d) Find the coordinates of the vertices of this conic (in the -coordinate system).
Whether the graph of the following equation is a parabola, an ellipse, or a hyperbola:
An equation of a conic section as, .
Compare the given equation of the conic with the general equation of the conic,
The quantity is known as discriminant of the above equation,
i. If , then the above equation is of hyperbola equation.
ii. If , then the above equation is of parabola equation.
iii. If , then the above equation is of an ellipse equation.
Given equation of conic is
The equation of the given conic after removing the -term, use the rotation of axes.
A graph of the equation .
The coordinates of the vertices of the conic .
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