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Find the locus of the midpoints of chord...

Find the locus of the midpoints of chords of hyperbola `3x^(2)-2y^(2)+4x-6y=0` parallel to y = 2x.

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To find the locus of the midpoints of chords of the hyperbola given by the equation \(3x^2 - 2y^2 + 4x - 6y = 0\) that are parallel to the line \(y = 2x\), we can follow these steps: ### Step 1: Rewrite the hyperbola equation First, we will rewrite the hyperbola equation in standard form. We can complete the square for both \(x\) and \(y\). The given equation is: \[ 3x^2 - 2y^2 + 4x - 6y = 0 ...
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