Q83.Let A, B and C be three points on the parabola y2 = 6x and let the line segment AB meet the line L through C parallel to the x-axis at the point D. Let M and N respectively be the feet of the perpendiculars from A and AM⋅BN 2 B on L. Then ( CD ) is equal to _________
What This Question Tests
The problem requires applying the parametric form of points on a parabola and using coordinate geometry to express lengths and ratios. Geometric interpretation of the given setup is crucial for simplification.
Concepts Tested
Formulas Used
y² = 4ax
Parametric coordinates (at², 2at)
📚 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?
6.11 — Dynamics Of Rotational
Physics Class 11 · Chapter 6
6.11 Dynamics of rotational the motion of extended bodies. motion about a fixed axis A large class of problems with extended bodies can be
2.2 — A Regular Hexagon Of Side 10 Cm Has A Charge 5 Mc At Each Of Its
Physics Class 11 · Chapter 2
2.2 A regular hexagon of side 10 cm has a charge 5 mC at each of its vertices. Calculate the potential at the centre of the hexagon.
📋 Question Details
- Chapter
- Parabola
- Topic
- Properties of parabola
- Year
- 2024
- Shift
- 09 Apr Shift 2
- Q Number
- Q83
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
More from this Chapter
Q95.The equation of a tangent to the parabola y2 = 8x is y = x + 2 . The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is (1) (−1, 1) (2) (0, 2) (3) (2, 4) (4) (−2, 0) y2 x2
Q80.A parabola has the origin as its focus and the line x = 2 as the directrix. Then the vertex of the parabola is at (1) (0, 2) (2) (1, 0) (3) (0, 1) (4) (2, 0)
Q69.If two tangents drawn from a point P to the parabola y2 = 4x are at right angles, then the locus of P is (1) 2x + 1 = 0 (2) x = −1 (3) 2x −1 = 0 (4) x = 1 =
Q70.Statement 1: y = mx − m1 is always a tangent to the parabola, y2 = −4x for all non-zero values of m. Statement 2: Every tangent to the parabola, y2 = −4x will meet its axis at a point whose abscissa is non- negative. (1) Statement 1 is true, Statement 2 is true; Statement 2 is a correct explanation of Statement 1. (2) Statement 1 is false, Statement 2 is true. (3) Statement 1 is true, Statement 2 is false. (4) Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation of Statement 1.