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If a, b, c form a geometric progression with common ratio r, then the sum of the ordinate of the point of intersection of the line $a x + b y + c = 0$ and the curve $x + 2 y^{2} = 2$

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$\frac{- r^{2}}{2}$

$\frac{- r}{2}$

$\frac{r}{2}$

$r$

answer is C.

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Detailed Solution

$b = a r a n d c = a r^{2}$

Put in $a x + b y + c = 0 \Rightarrow x = - r y - r^{2} p u t i n$

$x + 2 y^{2} = 2 \Rightarrow s u m o f o r d i n a t e = \frac{r}{2}$

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