Q84.Let E be an ellipse whose axes are parallel to the co-ordinates axes, having its centre at (3, −4), one focus at (4, −4) and one vertex at (5, −4). If mx −y = 4, m > 0 is a tangent to the ellipse E, then the value of 5m2 is equal to _____ .
What This Question Tests
This question requires determining the equation of an ellipse from its given center, focus, and vertex, and then applying the condition for a line to be tangent to the ellipse to find an unknown parameter.
Concepts Tested
Formulas Used
Equation of ellipse: (x-h)^2/a^2 + (y-k)^2/b^2 = 1
c = ae
b^2 = a^2(1-e^2)
Condition for tangency y=mx+c to x^2/a^2 + y^2/b^2 = 1 is c^2 = a^2m^2 + b^2
📚 NCERT Sections This Tests
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.
5.11 — Draw All The Isomers (Geometrical And Optical) Of:
Chemistry Class 11 · Chapter 5
5.11 Draw all the isomers (geometrical and optical) of: (i) [CoCl2(en)2] + (ii) [Co(NH3)Cl(en)2] 2+ (iii) [Co(NH3)2Cl2(en)]+
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
- Coordinate Geometry
- Topic
- Ellipse and Tangents
- Year
- 2021
- Shift
- 27 Jul Shift 2
- Q Number
- Q84
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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