AP EAMCET · Maths · Ellipse
The line \(x=m^2\) meets an ellipse \(9 x^2+y^2=9\) in the real and distinct points if and only if
- A \(|m|>1\)
- B \(|m| < 1\)
- C \(|m|>2\)
- D \(|m| < 2\)
Answer & Solution
Correct Answer
(B) \(|m| < 1\)
Step-by-step Solution
Detailed explanation
Since, the line \(x=m^2\) meets the ellipse \(9 x^2+y^2=9\) in the real and distinct points, so on solving line and ellipse, we get \(\begin{aligned} & 9 m^4+y^2=9 & \Rightarrow y^2=9\left(1-m^4\right) > 0 \\ \Rightarrow & m^4 < 1 & \Rightarrow|m| < 1 \end{aligned}\) Hence,…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- \(\lim _{n \rightarrow x} \sqrt{2}\left[\frac{(2+\sqrt{2})^n+(2-\sqrt{2})^n}{(2+\sqrt{2})-(2-\sqrt{2})^n}\right]=\)AP EAMCET 2022 Medium
- If the harmonic mean of the roots of the equation \(\sqrt{2} \mathrm{x}^2-\mathrm{bx}+(8-2 \sqrt{5})=0\) is 4, then the value of \(b\) isAP EAMCET 2025 Medium
- A discrete random variable takes values and , with probability respectively. Then the expected value of isAP EAMCET 2021 Easy
- If \(\omega\) is a complex cube root of unity, then
\(\sin \left[\left(\omega^{10}+\omega^{23}\right) \pi-\frac{\pi}{4}\right]=\)AP EAMCET 2023 Easy - If the angle between the circles \(x^2+y^2-4 x-6 y-3=0, x^2+y^2+8 x-4 y+\lambda=0\) is \(60^{\circ}\), then a value of \(\lambda\) isAP EAMCET 2017 Easy
- A random variable X follows a binomial distribution in which the difference between its mean and variance is 1. If \(2 \mathrm{P}(\mathrm{x}=2)=3 \mathrm{P}(\mathrm{x}=1)\), then \(\mathrm{n}^2 \mathrm{P}(\mathrm{x}>1)=\)AP EAMCET 2025 Medium
More PYQs from AP EAMCET
- If \(f: R \rightarrow R\) is an even function which is twice differentiable on \(R\) and \(f^{\prime \prime}(\pi)=1\), then \(f^{\prime \prime}(-\pi)\) is equal toAP EAMCET 2005 Medium
- Which of the following statements are correct?
I. In nitrating mixture nitric acid participates as an acid.
II. \(\sigma\) complex is the intermediate substance in electrophilic substitution of benzene.
III. Benzene on Friedel-Crafts alkylation with n-propyl chloride gives isopropyl benzene.AP EAMCET 2019 Medium - Benzamide \(\xrightarrow{\mathrm{Br}_2 / \mathrm{NaOH}} \mathrm{X} \xrightarrow[\text { alc. } \mathrm{KOH}]{\mathrm{CHCl}_3} \mathrm{Y}\)
The conversion of X to Y isAP EAMCET 2024 Medium - If \(\hat{i}-2 \hat{j}+3 \hat{k}, 2 \hat{i}+3 \hat{j}+\hat{k},-3 \hat{i}-\hat{j}-2 \hat{k}\) are the position vectors of three points A, B, C respectively, then \(\mathrm{A}, \mathrm{B}, \mathrm{C}\)AP EAMCET 2024 Easy
- Area of the triangle formed by the complex numbers \(\mathrm{z}, \mathrm{iz}\) and \(\mathrm{z}+\mathrm{iz}\) in the Argand diagram as vertices isAP EAMCET 2022 Medium
- The resistance of wire at \(0^{\circ} \mathrm{C}\) is \(20 \Omega\). If the temperature coefficient of the resistance is \(5 \times 10^{-3}{ }^{\circ} \mathrm{C}^{-1}\). The temperature at which the resistance will be double of that at \(0^{\circ} \mathrm{C}\) isAP EAMCET 2022 Medium