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  • If   form a G.P. with common ratio r, the sum of the ordinates of the po

If \mathrm{a, b, c}  form a G.P. with common ratio r, the sum of the ordinates of the points of intersection of the line \mathrm{a x+b y+c=0 }and the curve \mathrm{x+2 y^2=0 } is
 

Option: 1

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


Option: 2

\mathrm{\frac{-r}{2}}


Option: 3

\mathrm{\frac{r}{2}}


Option: 4

\mathrm{\frac{r^{2}}{2}}


Answers (1)

 The equation of the given line is \mathrm{a x+b y+c=0}

\mathrm{\Rightarrow \quad a x+a r y+a r^2=0 \quad \Rightarrow x+r y+r^2=0}

(i) intersects the curves \mathrm{x+2 y^2=0} at the points whose ordinates are given by

\mathrm{-2 y^2+r y+r^2=0 \text { or } 2 y^2-r y-r^2=0}

Therefore required sum of the ordinates =\mathrm{\frac{r}{2}}

Posted by

Ramraj Saini

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