Q66.Let a line L : 2x + y = k, k > 0 be a tangent to the hyperbola x2 −y2 = 3. If L is also a tangent to the parabola y2 = αx, then α is equal to: (1) 12 (2) −12 (3) 24 (4) −24
What This Question Tests
This question tests the ability to apply tangency conditions for a line to both a hyperbola and a parabola to find an unknown parameter.
Concepts Tested
Formulas Used
Condition for tangent y=mx+c to x^2/a^2 - y^2/b^2 = 1 is c^2 = a^2m^2 - b^2
Condition for tangent y=mx+c to y^2=4ax is c=a/m
📚 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.
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?
📋 Question Details
- Chapter
- Hyperbola
- Topic
- Tangent to hyperbola and parabola
- Year
- 2021
- Shift
- 22 Jul Shift 1
- Q Number
- Q66
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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Q72.Let P(3 sec θ, 2 tan θ) and Q(3 sec ϕ, 2 tan ϕ) where θ + ϕ = π2 , 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 −y24 = 1 (1) 11 3 (2) −113 (3) 13 2 (4) −132 = 5, then k is equal to: