Q68.If the area of an equilateral triangle inscribed in the circle x2 + y2 + 10x + 12y + c = 0 is 27√3 sq. units, then c is equal to: (1) 25 (2) 13 (3) −25 (4) 20
What This Question Tests
The question tests the ability to extract the radius from the general equation of a circle and then relate it to the area of an inscribed equilateral triangle to find the unknown constant 'c'.
Concepts Tested
Formulas Used
Equation of circle x^2+y^2+2gx+2fy+c=0
Radius R = sqrt(g^2+f^2-c)
Area of equilateral triangle = (3sqrt(3)/4)R^2
📚 NCERT Sections This Tests
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.
12.7 — The Radius Of The Innermost Electron Orbit Of A Hydrogen Atom Is
Physics Class 12 · Chapter 12
12.7 The radius of the innermost electron orbit of a hydrogen atom is 5.3×10–11 m. What are the radii of the n = 2 and n =3 orbits?
2.4 — A Spherical Conductor Of Radius 12 Cm Has A Charge Of 1.6 × 10–7C
Physics Class 11 · Chapter 2
2.4 A spherical conductor of radius 12 cm has a charge of 1.6 × 10–7C distributed uniformly on its surface. What is the electric field (a) inside the sphere (b) just outside the sphere (c) at a point 18 cm from the centre of the sphere?
📋 Question Details
- Chapter
- Circles
- Topic
- Properties of circles and inscribed triangles
- Year
- 2019
- Shift
- 10 Jan Shift 2
- Q Number
- Q68
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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