Q66.The locus of the mid points of the chords of the hyperbola x2 −y2 = 4, which touch the parabola y2 = 8x, is : (1) y2(x −2) = x3 (2) x3(x −2) = y2 (3) x2(x −2) = y3 (4) y3(x −2) = x2 lim n=1 n(n+1)x2+2(2n+1)x+4x ) is equal to :
What This Question Tests
This question combines concepts from hyperbola (midpoint of chord) and parabola (tangency condition) to find a locus, requiring careful algebraic elimination of parameters.
Concepts Tested
Formulas Used
Midpoint of chord formula T=S₁ for hyperbola
Condition for line y=mx+c to be tangent to y²=4ax is c=a/m
📚 NCERT Sections This Tests
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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.
9.8 — 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?
9.15 — 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.
📋 Question Details
- Chapter
- Hyperbola
- Topic
- Locus of midpoint of chords
- Year
- 2021
- Shift
- 26 Aug Shift 2
- Q Number
- Q66
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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