Find the shifted equation of $x^{2} + y^{2} = 49$ when the graph is shifted 3 units down and 2 units left.

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x^{2} + y^{2} - 4 x - 6 y = 36

x^{2} + y^{2} + 4 x + 6 y = 36

x^{2} + y^{2} + 4 x - 6 y = 36

x^{2} + y^{2} - 4 x + 6 y = 36

answer is A.

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Detailed Solution

The origin of the previous graph O(0,0) changes to A(−2,−3), new origin of the shifted graph.
For a fixed point (a,b) in the previous position of the graph changes to (c,d).
Then we can say c=a+2 and d=b+3. This gives a=c−2 and b=d−3.

a^{2} + b^{2} = 49

\Rightarrow {(c - 2)}^{2} + {(d - 3)}^{2} = 49

\Rightarrow x^{2} + y^{2} - 4 x - 6 y = 36

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