TS EAMCET · Maths · Sequences and Series
If \(a, b\) and \(c\) form a geometric progression with common ratio \(r\), then the sum of the ordinates of the points of intersection of the line \(a x+b y+c=0\) and the curve \(x+2 y^2=0\) is
- A \(-\frac{r^2}{2}\)
- B \(-\frac{r}{2}\)
- C \(\frac{r}{2}\)
- D \(r\)
Answer & Solution
Correct Answer
(C) \(\frac{r}{2}\)
Step-by-step Solution
Detailed explanation
Since, \(a, b\) and \(c\) form a geometric progression \(\therefore \quad a=a, b=a r, c=a r^2\) Therefore, given line becomes \(\begin{aligned} & a x+a r y+a r^2 & =0 \\ \Rightarrow & x+r y+r^2 & =0 \\ \Rightarrow & x & =-r y-r^2\end{aligned}\) On putting \(x=-r y-r^2\) in given…
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