Q72.If 5๐ฅ+ 9 = 0 is the directrix of the hyperbola 16๐ฅ2 - 9๐ฆ2 = 144, then its corresponding focus is: (1) -5, 0 (2) 5, 0 5 5 (3) - 3, 0 (4) 3, 0
What This Question Tests
This question is a direct application of the standard formulas for the directrix, focus, and eccentricity of a hyperbola given its equation.
Concepts Tested
Formulas Used
x^2/a^2 - y^2/b^2 = 1
Directrix: x = a/e
Focus: (ae, 0)
b^2 = a^2(e^2-1)
๐ NCERT Sections This Tests
2.1 โ Two Charges 5 ร 10โ8 C And โ3 ร 10โ8 C Are Located 16 Cm Apart. At
Physics Class 11 ยท Chapter 2
2.1 Two charges 5 ร 10โ8 C and โ3 ร 10โ8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
9.8 โ A Beam Of Light Converges At A Point P. Now A Lens Is Placed In The
Physics Class 12 ยท 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?
9.2 โ A 4.5 Cm Needle Is Placed 12 Cm Away From A Convex Mirror Of Focal
Physics Class 12 ยท Chapter 9
9.2 A 4.5 cm needle is placed 12 cm away from a convex mirror of focal length 15 cm. Give the location of the image and the magnification. Describe what happens as the needle is moved farther from the mirror.
๐ Question Details
- Chapter
- Hyperbola
- Topic
- Directrix and Focus of Hyperbola
- Year
- 2019
- Shift
- 10 Apr Shift 2
- Q Number
- Q72
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
More from this Chapter
Q96.For the hyperbola = 1 , which of the following remains constant when ฮฑ varies? cos2 ฮฑ ฮฑ โ sin2 (1) eccentricity (2) directrix (3) abscissae of vertices (4) abscissae of foci
Q71.If the eccentricity of a hyperbola x2 K 2 is = 1, which passes through (K, 2), is โ133 , then the value of 9 โy2b2 (1) 18 (2) 8 (3) 1 (4) 2
Q71.A tangent to the hyperbola x2 meets x-axis at P and y-axis at Q. Lines PR and QR are drawn such 4 โy22 = 1 that OPRQ is a rectangle (where O is the origin). Then R lies on : (1) 4 + 2 = 1 (2) 2 โ 4 = 1 x2 y2 x2 y2 (3) 2 + 4 = 1 (4) 4 โ 2 = 1 x2 y2 x2 y2
Q72.Let P(3 sec ฮธ, 2 tan ฮธ) and Q(3 sec ฯ, 2 tan ฯ) where ฮธ + ฯ = ฯ2 , be two distinct points on the hyperbola x2 . Then the ordinate of the point of intersection of the normals at P and Q is: 9 โy24 = 1 (1) 11 3 (2) โ113 (3) 13 2 (4) โ132 = 5, then k is equal to: