Q24.The focus of the parabola y2 = 4x + 16 is the centre of the circle C of radius 5 . If the values of λ, for which C passes through the point of intersection of the lines 3x −y = 0 and x + λy = 4, are λ1 and λ2, λ1 < λ2 , then 12λ1 + 29λ2 is equal to
What This Question Tests
This problem involves finding the focus of a parabola, using it as the center of a circle, and then determining parameters for the circle to pass through the intersection of two lines.
Concepts Tested
Formulas Used
y^2 = 4ax (parabola equation)
(x-h)^2 + (y-k)^2 = r^2 (circle equation)
📚 NCERT Sections This Tests
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?
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.
12.5 — A Hydrogen Atom Initially In The Ground Level Absorbs A Photon,
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
- Focus of parabola, circle equation, intersection of lines
- Year
- 2025
- Shift
- 23 Jan Shift 2
- Q Number
- Q24
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections; Class 11 Mathematics Ch 10: Straight Lines
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