Question

the curve xy=c^2 is a symmetric about​

Answer 1

Answer:

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Answer 2

The Main Answer is: The curve xy = c² is symmetric about the line y = -x

Given: the curve - xy = c²

To Find: Line about which the given curve is symmetric

Solution:

The given curve is an example of a Rectangular Hyperbola.

As shown in the figure, the curve is present in the 1st and 3rd quadrants due to the RHS (c²) being positive.

This means that the line of symmetricity of the curve xy = c² is in the 2nd and 3rd quadrants.

This line will be a straight line inclined equally from both the axes on their negative sides, i.e., forming an angle of 45° on both sides.

∴ Its slope (m) = tan(-45°) = -1

The equation of the line is y = mx

                                                    ⇒ y = -1 × x ⇒  y = -x

Therefore, the line of symmetricity of the graph xy = c² is y = -x.

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