Q67.The locus of the midpoints of the chord of the circle, x2 + y2 = 25 which is tangent to the hyperbola, x2 is : 9 −y216 = 1 (1) (x2 + y2)2 −16x2 + 9y2 = 0 (2) (x2 + y2)2 −9x2 + 144y2 = 0 2 2 (3) (x2 + y2) −9x2 −16y2 = 0 (4) (x2 + y2) −9x2 + 16y2 = 0
What This Question Tests
This question combines concepts from circles and hyperbolas, requiring the student to find the locus of a midpoint of a chord that is simultaneously tangent to a hyperbola.
Concepts Tested
Formulas Used
T = S1 (for chord with midpoint)
y = mx +/- sqrt(a^2m^2 - b^2) (tangent to hyperbola x^2/a^2 - y^2/b^2 = 1)
📚 NCERT Sections This Tests
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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:
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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
- Circles
- Topic
- Locus of midpoints of chords
- Year
- 2021
- Shift
- 16 Mar Shift 1
- Q Number
- Q67
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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