TS EAMCET · Maths · Parabola
Study the following statements. \(\Upsilon\). The vertex of the parabola \[ x=l^2+m y+n i s\left(n-\frac{m^2}{4 l},-\frac{m}{2 l}\right) \] M. The focus of the parabola \(y=l x^2+m x+n\) is \(\left(n+\frac{1-m^2}{4 l},-\frac{m}{2 l}\right)\) m. The pole of the line \(l x+m y+n=0\) with respect to the parabola \(x^2=4\) ay is \[ \left(-\frac{2 a l}{m}, \frac{n}{m}\right) \] Then, the correct option among the following is
- A All the three statements are true
- B Statements I \& II are true but III is false
- C Statements I \& III are true but II is false
- D Statements II \& III are true but I is false
Answer & Solution
Correct Answer
(C) Statements I \& III are true but II is false
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { (I) } x=y^2+m y+n \\ & \Rightarrow \quad y^2+\frac{m}{l} y=\frac{x}{l}-\frac{n}{l} \\ & \Rightarrow \quad y^2+\frac{m}{l} y+\frac{m^2}{4 l^2}=\frac{x}{l}-\frac{n}{l}+\frac{m^2}{4 l^2} \\ & \Rightarrow \quad\left(y+\frac{m}{2…
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