Q77.A differential equation representing the family of parabolas with axis parallel to y−axis and whose length of latus rectum is the distance of the point (2, −3) from the line 3x + 4y = 5, is given by: (1) 11 d2x dy2 = 10 (2) 11 dx2d2y = 10 d2y (3) 10 = 11 (4) 10 d2xdy2 = 11 dx2 = 1 and
What This Question Tests
This question requires forming a differential equation by first finding the length of the latus rectum using the distance formula, then setting up the general equation of the parabola and eliminating arbitrary constants through differentiation.
Concepts Tested
Formulas Used
Equation of parabola with axis parallel to y-axis: (x-h)² = 4a(y-k)
Length of latus rectum = |4a|
Distance of point (x0,y0) from Ax+By+C=0 is |Ax0+By0+C|/√(A²+B²)
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📋 Question Details
- Chapter
- Differential Equations
- Topic
- Formation of Differential Equations
- Year
- 2021
- Shift
- 27 Aug Shift 2
- Q Number
- Q77
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 9: Differential Equations
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