Q72.A normal to the hyperbola, 4x2 −9y2 = 36 meets the co-ordinate axes x and y at A and B, respectively. If the parallelogram OABP(O being the origin) is formed, then the locus of P is (1) 4x2 −9y2 = 121 (2) 4x2 + 9y2 = 121 (3) 9x2 −4y2 = 169 (4) 9x2 + 4y2 = 169
What This Question Tests
This problem involves finding the equation of a normal to a hyperbola, determining its intercepts with the axes, and then deriving the locus of the fourth vertex of a parallelogram formed by these points and the origin.
Concepts Tested
Formulas Used
Equation of normal to x²/a² - y²/b² = 1 at (x1, y1) is a²x/x1 + b²y/y1 = a²+b²
Midpoint formula
📚 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.
9.15 — Apply Mirror Equation And The Condition:
Physics Class 12 · Chapter 9
9.15 Apply mirror equation and the condition: (a) f < 0 (concave mirror); u < 0 (object on left) (b) f > 0; u < 0 (c) f > 0 (convex mirror) and u < 0 (d) f < 0 (concave mirror); f < u < 0 to deduce the desired result.
📋 Question Details
- Chapter
- Hyperbola
- Topic
- Normal to hyperbola, Locus
- Year
- 2018
- Shift
- 15 Apr Shift 2 Online
- Q Number
- Q72
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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