Circle $x^2+y^2=1 \rightarrow x^2-y^2=1 $ Given linear transformation above, I need to find the standard matrix (2*2) of such linear transformation. (If there is no such transformation matrix, i need to explain why)
2026-03-25 09:37:13.1774431433
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Linear Transformation of Circle to Hyperbola
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Hint: How do linear transformations affect area? That is, if a linear transformation, with matrix $M$, carries $A$, $B$, $C$ to $A^\prime$, $B^\prime$, $C^\prime$, then how is the area of $\triangle ABC$ related to the area of $\triangle A^\prime B^\prime C^\prime$? Then: What can you say about areas of triangles inscribed in a circle vs inscribed on a hyperbola?
just a hint
A point of the circle $x^2+y^2=1$ is $(\cos (t),\sin (t)) $.
A point of the hyerbola $x^2-y^2=1$ is $(\cosh (t),\sinh (t)) .$