JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
The parabolas : \(a^2+2 b x+c y=0\) and \(d x^2+2 ex + fy =0\) intersect on the line \(y=1\). If \(a, b, c, d, e, f\) are positive real numbers and \(a , b , c\) are in \(G.P.\), then
- A \(d, e, f\) are in \(A.P.\)
- B \(\frac{ d }{ a }, \frac{ e }{ b }, \frac{ f }{ c }\) are in \(G.P.\)
- C \(\frac{ d }{ a }, \frac{ e }{ b }, \frac{ f }{ c }\) are in \(A.P.\)
- D \(d, e, f\) are in \(G.P. \)
Answer & Solution
Correct Answer
(C) \(\frac{ d }{ a }, \frac{ e }{ b }, \frac{ f }{ c }\) are in \(A.P.\)
Step-by-step Solution
Detailed explanation
\(a x^2+2 b x+c=0\) \(\Rightarrow ax ^2+2 \sqrt{ ac } c + c =0\left(\because b ^2= ac \right)\) \(\Rightarrow( x \sqrt{ a }+\sqrt{ c })^2=0\) \(x^2-\frac{\sqrt{c}}{\sqrt{a}}\) Now, \(dx ^2+2 ex + f =0\)…
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