Q71.If the eccentricity of the standard hyperbola passing through the point ( 4,6 ) is 2, then the equation of the tangent to the hyperbola at ( 4,6 ) is: (1) 2๐ฅ- 3๐ฆ+ 10 = 0 (2) ๐ฅ- 2๐ฆ+ 8 = 0 (3) 3๐ฅ- 2๐ฆ= 0 (4) 2๐ฅ- ๐ฆ- 2 = 0 1 1 + ๐3 + ๐ฅ- ๐3 ๐ฅ
What This Question Tests
The question involves finding the equation of a hyperbola given its eccentricity and a point it passes through, and then deriving the equation of the tangent at that specific point.
Concepts Tested
Formulas Used
Equation of hyperbola x^2/a^2 - y^2/b^2 = 1
e^2 = 1 + b^2/a^2
Equation of tangent to x^2/a^2 - y^2/b^2 = 1 at (x1,y1): x x1/a^2 - y y1/b^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.
9.15 โ Apply Mirror Equation And The Condition:
Physics Class 12 ยท 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.
2.5 โ A Parallel Plate Capacitor With Air Between The Plates Has A
Physics Class 11 ยท Chapter 2
2.5 A parallel plate capacitor with air between the plates has a capacitance of 8 pF (1pF = 10โ12 F). What will be the capacitance if the distance between the plates is reduced by half, and the space between them is filled with a substance of dielectric constant 6?
๐ Question Details
- Chapter
- Hyperbola
- Topic
- Equation of hyperbola, eccentricity, tangent to hyperbola
- Year
- 2019
- Shift
- 08 Apr Shift 2
- Q Number
- Q71
- 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 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: