Q71.If the parabolas y2 = 4b(x −c) and y2 = 8ax have a common normal, then which one of the following is a valid choice for the ordered triad (a, b, c) (1) (1, 1, 3) (2) ( 12 , 2, 0) (3) ( 12 , 2, 3) (4) All of above
What This Question Tests
This question tests the understanding of normals to parabolas and the conditions for two parabolas to have a common normal, requiring algebraic manipulation to find a consistent set of parameters.
Concepts Tested
Formulas Used
Equation of normal to y^2=4ax: y=mx-2am-am^3
Equation of normal to y^2=4b(x-c): y=m(x-c)-2bm-bm^3
📚 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.
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
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
- Parabola
- Topic
- Common normal to parabolas
- Year
- 2019
- Shift
- 10 Jan Shift 1
- Q Number
- Q71
- Type
- MCQ
- 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.