If a, b, c form a G.P., then twice the sum of the ordinates of the points of intersection of the line ax $$+$$ by $$+$$ c $$=$$ $$0$$ and the curve x $$+$$ $$2y2$$ $$=$$ $$0$$ is

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Let a, b, c be in G.P. with common ratio r.Then, b $$=$$ ar and c $$=$$ $$ar2$$.So, the equation of the line is ax $$+$$ by $$+$$ c $$=$$ $$0$$⇒ ax $$+$$ ary $$+$$ $$ar2$$ $$=$$ $$0$$ ⇒ x $$+$$ ry $$+$$ $$r2$$ $$=$$ $$0This$$ line cuts the curve x $$+$$ $$2y2$$ $$=$$ $$0Eliminating$$ x, we get $$2y2$$ – ry $$+$$ $$r2$$ $$=$$ $$0If$$ the roots of the quadratic equation are $$y1$$ and $$y2$$, $$theny1+y2=r2$$⇒$$2y1+y2=r=ba=cb$$

If a, b, c form a G.P., then twice the sum of the ordinates of the points of intersection of the line ax + by + c = 0 and the curve x + 2y² = 0 is

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If a, b, c form a G.P., then twice the sum of the ordinates of the points of intersection of the line ax + by + c = 0 and the curve x + 2y2 = 0 is

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If a, b, c form a G.P., then twice the sum of the ordinates of the points of intersection of the line ax + by + c = 0 and the curve x + 2y² = 0 is