AP EAMCET · Maths · Ellipse
The eccentricity of an ellipse, with its centre as origin, is \(1 / 2\). If one of the directrices is \(x=4\), then the equation of the ellipse is given by
- A \(4 x^2+y^2=12\)
- B \(x^2+3 y^2=12\)
- C \(4 x^2+3 y^2=12\)
- D \(3 x^2+4 y^2=12\)
Answer & Solution
Correct Answer
(D) \(3 x^2+4 y^2=12\)
Step-by-step Solution
Detailed explanation
Centre \(=(0,0)\) Eccentricity \((\mathrm{e})=\frac{1}{2}\) Equation of directrix is \(x=4\) \(\Rightarrow \frac{a}{e}=4\) \(\Rightarrow a=4 e\) \(\Rightarrow a=2\) \(\begin{aligned} b^2 & =a^2\left(1-e^2\right) \\ & =4\left(1-\frac{1}{4}\right) \\ b^2 & =3 \end{aligned}\)…
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
- \(\int_0^\pi \frac{1}{1+\sin x} d x\) is equal toAP EAMCET 2009 Medium
- If a committee of 10 members is to be formed from 8 men and 6 women, then the number of different possible committees in which the men are in majority isAP EAMCET 2024 Medium
- The equation of the circle whose diameter is the common chord of the circles \(x^2+y^2+2 x+3 y+1=0\) and \(x^2+y^2+4 x+3 y+2=0\) isAP EAMCET 2019 Medium
- The area (is sq. units) bounded by the curves \(x=y^2\) and \(x=3-2 y^2\) isAP EAMCET 2024 Easy
- AP EAMCET 2018 Hard
- If \(\sqrt{-3-4 i}=\mathrm{re}^{\mathrm{i} \theta}\), then \(\mathrm{r}^2 \tan \theta=\)AP EAMCET 2023 Hard
More PYQs from AP EAMCET
- A man of \(50 \mathrm{~kg}\) is standing at one end on a boat of length \(25 \mathrm{~m}\) and mass \(200 \mathrm{~kg}\). If he starts running and when he reaches the other end, he has a velocity \(2 \mathrm{~ms}^{-1}\) with respect to the boat. The final velocity of the boat is : (in \(\mathrm{ms}^{-1}\) )AP EAMCET 2006 Easy
- The rate of reaction of \(t\)-butyl bromide and . \(\mathrm{NaOH}\) in water depends on the concentration ofAP EAMCET 2022 Easy
- If \(x_n=\cos \left(\frac{\pi}{4^n}\right)+i \sin \left(\frac{\pi}{4^n}\right)\), then \(x_1 x_2 x_3 \ldots \infty\) is equal toAP EAMCET 2002 Hard
- If \(\mathrm{A}\) and \(\mathrm{B}\) are symmetric matrices of same order such that \(\mathrm{AB}+\mathrm{BA}=\mathrm{X}\) and \(\mathrm{AB}-\mathrm{BA}=\mathrm{Y}\), then \((\mathrm{XY})^{\mathrm{T}}=\)AP EAMCET 2022 Medium
- Between the plates of a parallel plate capacitor of plate area \(\mathrm{A}\) and capacity \(0.025 \mu \mathrm{F}\), a metal plate of area, \(\mathrm{A}\) and thickness equal to \(\frac{1}{3}\) of the separation between the plates of the capacitor is introduced. If the capacitor is charged to \(100 \mathrm{~V}\), then the amount of work done to remove the metal plate from the capacitor isAP EAMCET 2023 Hard
- If \(b+c=3 a\), then \(\cot \frac{B}{2} \cot \frac{C}{2}\) is equal to :AP EAMCET 2006 Hard