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# The midpoint of a chord of the ellipse $x^2+4y^2-2x+20 y=0$ is $(2,-4)$. The equation of the chord is?

$(a)\;x-6y=26 \quad (b)\;x+6y=26 \quad (c)\;6x-y=26 \quad (d)\;6x+y=26$

<div class="clay6-step-odd"><div class="clay6-basic" id="pr10">$(a)\;x-6y=26$  is the correct answer  since $(2,-4)$  is the midpoint, </div><div class="clay6-basic" id="pr11">it  lies on the line of chord.</div><div class="clay6-basic" id="pr12">$\Rightarrow\:$ (2,-4)$should satisfy the equation of the chord.</div><div class="clay6-basic" id="pr13">But$(2,-4)$satisfies only equation$x-6y=26$out of the$4$options.</div><div class="clay6-basic" id="pr14">$\therefore (a)  is the correct answer.</div></div>
edited Mar 27, 2014