Q67.A tangent and a normal are drawn at the point P(2, −4) on the parabola y2 = 8x, which meet the directrix of the parabola at the points A and B respectively. If Q(a, b) is a point such that AQBP is a square, then 2a + b is equal to (1) −12 (2) −20 (3) −16 (4) −18
What This Question Tests
This problem involves multiple steps: finding equations of tangent/normal to a parabola, their intersection with the directrix, and then using geometric properties of a square to find coordinates.
Concepts Tested
Formulas Used
Tangent to y^2=4ax at (x1,y1): yy1 = 2a(x+x1)
Normal to y^2=4ax at (x1,y1): y-y1 = (-y1/2a)(x-x1)
Directrix of y^2=4ax: x = -a
Midpoint formula
📚 NCERT Sections This Tests
2.3 — Two Charges 2 Mc And –2 Mc Are Placed At Points A And B 6 Cm
Physics Class 11 · Chapter 2
2.3 Two charges 2 mC and –2 mC are placed at points A and B 6 cm apart. (a) Identify an equipotential surface of the system. (b) What is the direction of the electric field at every point on this surface?
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.
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?
📋 Question Details
- Chapter
- Coordinate Geometry
- Topic
- Parabola, Tangents and Normals
- Year
- 2021
- Shift
- 27 Aug Shift 1
- Q Number
- Q67
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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