Q72.The normal at (2, 23 ) to the ellipse, x216 + y23 = 1 touches a parabola, whose equation is (1) y2 = −104x (2) y2 = 14x (3) y2 = 26x (4) y2 = −14x sin(π cos2 x)
What This Question Tests
This question tests the ability to find the equation of a normal to an ellipse at a given point and then apply the condition for a line to be tangent to a parabola. It requires careful calculation and formula application.
Concepts Tested
Formulas Used
Normal to x²/a² + y²/b² = 1 at (x₁, y₁): a²x/x₁ - b²y/y₁ = a² - b²
Condition for y = mx + c to be tangent to y² = 4Ax: c = A/m
📚 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.
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.
14.2 — Which Of The Statements Given In Exercise 14.1 Is True For P-Type
Physics Class 12 · Chapter 14
14.2 Which of the statements given in Exercise 14.1 is true for p-type semiconductos.
📋 Question Details
- Chapter
- Coordinate Geometry
- Topic
- Normal to Ellipse & Tangent to Parabola
- Year
- 2012
- Shift
- 26 May Online
- Q Number
- Q72
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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