Q67.If the line 𝑥- 1 = 0, is a directrix of the hyperbola 𝑘𝑥2 - 𝑦2 = 6, then the hyperbola passes through the point (1) -2√5, 6 (2) -√5, 3 (3) √5, - 2 (4) 2√5, 3√6
What This Question Tests
This question requires converting the given hyperbola equation to standard form, using the directrix information to find eccentricity, and then checking which point satisfies the hyperbola equation.
Concepts Tested
Formulas Used
x²/a² - y²/b² = 1
e = √(1 + b²/a²)
Directrix x = a/e
📚 NCERT Sections This Tests
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
Physics Class 11 · Chapter 2
2.1 Two charges 5 × 10–8 C and –3 × 10–8 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.
9.15 — Apply Mirror Equation And The Condition:
Physics Class 12 · Chapter 9
9.15 Apply mirror equation and the condition: (a) f < 0 (concave mirror); u < 0 (object on left) (b) f > 0; u < 0 (c) f > 0 (convex mirror) and u < 0 (d) f < 0 (concave mirror); f < u < 0 to deduce the desired result.
10.2 — What Is The Shape Of The Wavefront In Each Of The Following Cases:
Physics Class 12 · Chapter 10
10.2 What is the shape of the wavefront in each of the following cases: (a) Light diverging from a point source. (b) Light emerging out of a convex lens when a point source is placed at its focus. (c) The portion of the wavefront of light from a distant star intercepted by the Earth.
📋 Question Details
- Chapter
- Hyperbola
- Topic
- Directrix of a hyperbola
- Year
- 2022
- Shift
- 26 Jul Shift 2
- Q Number
- Q67
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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Q96.For the hyperbola = 1 , which of the following remains constant when α varies? cos2 α α − sin2 (1) eccentricity (2) directrix (3) abscissae of vertices (4) abscissae of foci
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