WBJEE · Maths · Ellipse
The line \(\mathrm{y}=2 \mathrm{t}^2\) intersects the ellipse \(\frac{x^2}{9}+\frac{y^2}{4}=1\) in real points if
- A \(|t| \leq 1\)
- B \(|t| < 1\)
- C \(|t|>1\)
- D \(|t| \geq 1\)
Answer & Solution
Correct Answer
(A) \(|t| \leq 1\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Hints: } \frac{x^2}{9}+\frac{y^2}{4}=1 ; \mathrm{y}=2 \mathrm{t}^2 \\ & \frac{x^2}{9}+\frac{4 t^4}{4}=1 \Rightarrow \frac{x^2}{9}+t^4=1 \Rightarrow x^2=9\left(1-t^4\right) \\ & x^2 \geq 0 \Rightarrow 9\left(1-t^4\right) \geq 0 \Rightarrow t^4-1 \leq 0…
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