How do you identify the following equation $x^{2} + y^{2} = 16$ $x^2 + y^2 = 16$ as that of a line, a circle, an ellipse, a parabola, or a hyperbola.?

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How do you identify the following equation $x^{2} + y^{2} = 16$ $x^2 + y^2 = 16$ as that of a line, a circle, an ellipse, a parabola, or a hyperbola.?

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Answer 1 · 2016-03-25T13:19:53

The equation is that of a circle

Explanation:

First, move all terms on 1 side of the equation...
The equation will be in the form

$a x^{2} + b y^{2} + c x + d y + e = 0$ $ax^2 + by^2 +cx + dy + e = 0$

If both $a$ $a$ and $b$ $b$ are 0, then we are dealing with a line.
If either $a$ $a$ or $b$ $b$ is 0 (but not both), then we are dealing with a parabola.
If $a$ $a$ and $b$ $b$ have different signs, then we are dealing with a hyperbola
If $a$ $a$ and $b$ $b$ are equal, then we are dealing with a circle
If $a$ $a$ and $b$ $b$ have the same signs but with different absolute value, then we are dealing with an ellipse

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How do you identify the following equation $x^{2} + y^{2} = 16$ $x^2 + y^2 = 16$ as that of a line, a circle, an ellipse, a parabola, or a hyperbola.?

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

How do you identify the following equation x2+y2=16x^2 + y^2 = 16 as that of a line, a circle, an ellipse, a parabola, or a hyperbola.?

1 Answer

Explanation:

Related questions

Impact of this question

How do you identify the following equation $x^{2} + y^{2} = 16$ $x^2 + y^2 = 16$ as that of a line, a circle, an ellipse, a parabola, or a hyperbola.?