Q83.If the length of the latus rectum of the ellipse x2 + 4y2 + 2x + 8y −λ = 0 is 4 , and l is the length of its major axis, then λ + l is equal to _____. . Let the major
What This Question Tests
This question tests the ability to transform a general equation into the standard form of an ellipse, then apply formulas for the length of the latus rectum and major axis to find unknown parameters.
Concepts Tested
Formulas Used
(x-h)^2/a^2 + (y-k)^2/b^2 = 1
Length of latus rectum = 2b^2/a (if a>b)
Length of major axis = 2a (if a>b)
📚 NCERT Sections This Tests
9.8 — A Beam Of Light Converges At A Point P. Now A Lens Is Placed In The
Physics Class 12 · Chapter 9
9.8 A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12cm from P. At what point does the beam converge if the lens is (a) a convex lens of focal length 20cm, and (b) a concave lens of focal length 16cm?
9.19 — A Screen Is Placed 90Cm From An Object. The Image Of The Object On
Physics Class 12 · Chapter 9
9.19 A screen is placed 90cm from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by 20cm. Determine the focal length of the lens.
12.5 — A Hydrogen Atom Initially In The Ground Level Absorbs A Photon,
Physics Class 12 · Chapter 12
12.5 A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of photon.
📋 Question Details
- Chapter
- Ellipse
- Topic
- Properties of ellipse
- Year
- 2022
- Shift
- 27 Jul Shift 1
- Q Number
- Q83
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
More from this Chapter
Q81.A focus of an ellipse is at the origin. The directrix is the line x = 4 and the eccentricity is 1/2. Then the length of the semi-major axis is (1) 8 (2) 2 3 3 (3) 4 (4) 5 3 3
Q69.Equation of the ellipse whose axes are the axes of coordinates and which passes through the point (−3, 1) and has eccentricity is √25 (1) 5x2 + 3y2 −48 = 0 (2) 3x2 + 5y2 −15 = 0 (3) 5x2 + 3y2 −32 = 0 (4) 3x2 + 5y2 −32 = 0 Q70.$$ \lim _{x \rightarrow 2}\left(\frac{\sqrt{1-\cos \{2(x-2)\}}}{x-2}\right) (1) equals √2 (2) equals −√2 (3) equals 1 (4) does not exist √2
Q69.If P1 and P2 are two points on the ellipse x24 + y2 = 1 at which the tangents are parallel to the chord joining the points (0, 1) and (2, 0), then the distance between P1 and P2 is (1) 2√2 (2) √5 (3) 2√3 (4) √10
Q72.An ellipse is drawn by taking a diameter of the circle (x −1)2 + y2 = 1 as its semiminor axis and a diameter of the circle x2 + (y −2)2 = 4 as its semi-major axis. If the centre of the ellipse is the origin and its axes are the coordinate axes, then the equation of the ellipse is (1) 4x2 + y2 = 4 (2) x2 + 4y2 = 8 (3) 4x2 + y2 = 8 (4) x2 + 4y2 = 16