COMEDK · Maths · 14. Ellipse
The equation of an ellipse, whose focus is \((1,0)\), directrix is \(x=4\) and whose eccentricity is a root of the quadratic equation \(2 x^2-3 x+1=0\), is
- A \(\dfrac{x^2}{3}+\dfrac{y^2}{8}=1\)
- B \(\dfrac{x^2}{4}+\dfrac{y^2}{3}=1\)
- C \(\dfrac{x^2}{3}+\dfrac{y^2}{4}=1\)
- D \(\dfrac{x^2}{2}+\dfrac{y^2}{3}=1\)
Answer & Solution
Correct Answer
(B) \(\dfrac{x^2}{4}+\dfrac{y^2}{3}=1\)
Step-by-step Solution
Detailed explanation
The given quadratic equation is \(2e^2 - 3e + 1 = 0\). Solving for \(e\): \(2e^2 - 2e - e + 1 = 0 \Rightarrow 2e(e - 1) - 1(e - 1) = 0 \Rightarrow (2e - 1)(e - 1) = 0\). The roots are \(e = 1\) or \(e = 1/2\). Since the curve is an ellipse, \(e < 1\), so \(e = 1/2\). Let the…
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
- \(A\) and \(B\) are two matrices such that \(A B=B\), \(B A=A\), then \(A^{2}+B^{2}=\)COMEDK 2014 Medium
- Let point Q be the image of point \(P(2, -1)\) in the line \(3x + 5 = 4y\). Find the area of the circle that has the segment PQ as the diameter.COMEDK 2026 Medium
- The probability of inviting three friends on 5 consecutive days, exactly one friend a day and no friend is invited on more than two days isCOMEDK 2024 Medium
- If two vertices of a triangle are \((3,-2)\) and \((-2,3)\) and its orthocentre is \((-6,1)\).
Then the difference between ordinate and abscissa of the third vertex of the triangle isCOMEDK 2025 Medium - The differential coefficient is \(f(\sin x)\) with respect to \(x\) where \(f(x)+\log x\) isCOMEDK 2013 Easy
- A die is thrown twice and the sum of numbers appearing is observed to be 8 . What is the conditional probability that the number 5 has appeared atleast once?COMEDK 2023 Medium
More PYQs from COMEDK
- Output of an \(A C\) source is \(V=100 \sin 100 \pi t \cos\) \(100 \pi t\). Which of these are correct?COMEDK 2024 Easy
- A ray of light incident on one face of an equilateral prism at \(60^{\circ}\) enters and leaves the prism symmetrically. Refractive index of the prism material isCOMEDK 2016 Medium
- An ideal gas goes from state \(A\) to state \(B\) via three different processes as indicated in the \(p\)-\(V\) diagram. If \(Q_1, Q_2\) and \(Q_3\) indicate the heat absorbed by the three processes and \(\Delta U_1, \Delta U_2\) and \(\Delta U_3\) indicate the change in internal energy along the three processes respectively, then
COMEDK 2023 Medium - The charges \(Q,+q\) and \(+q\) are placed at the vertices of an equilateral triangle of side \(l\). If the net electrostatic potential energy of the system is zero, then \(Q\) is equal toCOMEDK 2018 Easy
- A wire of \(24 \Omega\) resistance is bent to form a square loop. A 10 V battery negligible internal resistance is connected across the diagonals of the square loop. The potential drop across one of its sides is:COMEDK 2025 Medium
- \(\int_{0}^{\pi / 2} \log (\tan x) d x=\)COMEDK 2018 Easy