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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?

\[(a)\;x-6y=26 \quad (b)\;x+6y=26 \quad (c)\;6x-y=26 \quad (d)\;6x+y=26 \]
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<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>
answered Nov 7, 2013 by pady_1
edited Mar 27, 2014 by rvidyagovindarajan_1
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