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Chapter 6: Problem 63

Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $$25 x^{2}-10 x-200 y-119=0$$

Short Answer

Expert verified
The graph of the given equation is a parabola.

Step by step solution

01

Rearrange the equation

The equation needs to be rearranged, so that it fits one of the standard forms. This implies factorization and reordering terms, which leads to \(25(x-0.2)^{2}-200(y+0.3)=0\).
02

Transform to standard form

Dividing the whole equation by 25, the equation switches to \((x-0.2)^{2}-8(y+0.3)=0\) . Now, this equation can be transformed into the standard equation for a parabola \(y=a(x-h)^{2}+k\) by setting \(a=-8\), \(h=0.2\), and \(k=-0.3\).
03

Classification

Now that the equation is in the standard form of a parabola, it can be classified. The equation is clearly a parabola because it fits the standard parabola equation.

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