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The parabola with directrix \(x+2 y-1=0\) and focus \((1,0)\) is
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Verified Answer
The correct answer is:
\(4 x^2-4 x y+y^2-8 x+4 y+4=0\)
Equation of parabola having directrix \(x+2 y-1=0\) and focus \((1,0)\) is
\(\begin{aligned}
& \frac{|x+2 y-1|}{\sqrt{1+4}}=\sqrt{(x-1)^2+(y-0)^2} \\
\Rightarrow \quad & (x+2 y-1)^2=5\left[(x-1)^2+y^2\right] \\
\Rightarrow \quad & x^2+4 y^2+1+4 x y-2 x-4 y=5 \\
& \quad\left(x^2+y^2-2 x+1\right) \\
\Rightarrow \quad & 4 x^2-4 x y+y^2-8 x+4 y+4=0
\end{aligned}\)
Hence, option (a) is correct.
\(\begin{aligned}
& \frac{|x+2 y-1|}{\sqrt{1+4}}=\sqrt{(x-1)^2+(y-0)^2} \\
\Rightarrow \quad & (x+2 y-1)^2=5\left[(x-1)^2+y^2\right] \\
\Rightarrow \quad & x^2+4 y^2+1+4 x y-2 x-4 y=5 \\
& \quad\left(x^2+y^2-2 x+1\right) \\
\Rightarrow \quad & 4 x^2-4 x y+y^2-8 x+4 y+4=0
\end{aligned}\)
Hence, option (a) is correct.
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