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If \((h, k)\) be the point to which the origin has to be shifted in order to get the transformed equation of \(y^2-4 x+6 y+17=0\) as \(y^2=4 a x\), then \(h^2+k^2=\)
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The correct answer is:
13
Given equation is \(y^2-4 x+6 y+17=0\)
\(\Rightarrow \quad(y+3)^2=4(x-2)\)
If origin is shifted to the point \((2,-3)\), then the equation \(y^2-4 x+6 y+17=0\) get transformed as \(y^2=4 a x\).
So, \(\quad(h, k)=(2,-3)\)
\(\therefore h^2+k^2=4+9=13\)
Hence, option (d) is correct.
\(\Rightarrow \quad(y+3)^2=4(x-2)\)
If origin is shifted to the point \((2,-3)\), then the equation \(y^2-4 x+6 y+17=0\) get transformed as \(y^2=4 a x\).
So, \(\quad(h, k)=(2,-3)\)
\(\therefore h^2+k^2=4+9=13\)
Hence, option (d) is correct.
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