Q85.The differential equation representing the family of ellipses having foci either on the x-axis or on the y-axis, center at the origin and passing through the point (0, 3) is (1) xyy′ −y2 + 9 = 0 (2) xyy′′ + x(y′)2 −yy′ = 0 (3) xyy′ + y2 −9 = 0 (4) x + yy′′ = 0 → → → →
What This Question Tests
This question involves forming a differential equation from the general equation of an ellipse, considering two cases for foci, and then eliminating the arbitrary constants after using a given point to constrain the equation.
Concepts Tested
Formulas Used
Equation of ellipse: x²/a² + y²/b² = 1 (foci on x-axis), y²/a² + x²/b² = 1 (foci on y-axis)
📚 NCERT Sections This Tests
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📋 Question Details
- Chapter
- Differential Equations
- Topic
- Formation of differential equations
- Year
- 2018
- Shift
- 16 Apr Online
- Q Number
- Q85
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 9: Differential Equations
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