Q83.If two tangents drawn from a point (α, β) lying on the ellipse 25x2 + 4y2 = 1 to the parabola y2 = 4x are such that the slope of one tangent is four times the other, then the value of (10α + 5)2 + (16β2 + 50)2 equals ______
What This Question Tests
This is a complex problem integrating tangents to a parabola, points on an ellipse, and a specific relationship between tangent slopes, requiring extensive algebraic manipulation.
Concepts Tested
Formulas Used
Tangent to y²=4ax is y=mx+a/m
Equation of ellipse x²/A² + y²/B² = 1
📚 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.
2.5 — A Parallel Plate Capacitor With Air Between The Plates Has A
Physics Class 11 · Chapter 2
2.5 A parallel plate capacitor with air between the plates has a capacitance of 8 pF (1pF = 10–12 F). What will be the capacitance if the distance between the plates is reduced by half, and the space between them is filled with a substance of dielectric constant 6?
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Physics Class 12 · Chapter 12
12.5 A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of photon.
📋 Question Details
- Chapter
- Parabola
- Topic
- Tangents to parabola and ellipse
- Year
- 2022
- Shift
- 24 Jun Shift 1
- Q Number
- Q83
- Type
- Multi concept
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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