What does the equation (x - a)^2 + (y - b)^2 = r^2 become when th… - Vidyadip

Question

What does the equation $(x - a)^2 + (y - b)^2 = r^2$ become when the axes are transferred to parallel axes through the point (a - c, b)?

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Answer

We have, $(x-a)^2+(y-b)^2=r^2 \ldots .$. (i) Substituting $x=x+(a-c), y=y+b$ in the equcation(i), we get $[x+a-c-a]^2+$ $[y+b-b]^2=r^2 \Rightarrow[x-c]^2+[y]^2=r^2 \Rightarrow x^2+c^2-2 x c+y^2=r^2 \Rightarrow x^2+y^2-2 x c=r^2-c^2$ Hence, the required equation is $x^2+y^2-2 x c=r^2-c^2$

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