Q76.If two vertices of an equilateral triangle are A(−a, 0) and B(a, 0), a > 0, and the third vertex C lies above x- axis then the equation of the circumcircle of △ABC is : (1) 3x2 + 3y2 −2√3ay = 3a2 (2) 3x2 + 3y2 −2ay = 3a2 (3) x2 + y2 −2ay = a2 (4) x2 + y2 −√3ay = a2
What This Question Tests
This question tests the ability to determine the coordinates of the third vertex of an equilateral triangle given two vertices, then find its circumcenter and circumradius using geometric properties, and finally write the equation of the circumcircle.
Concepts Tested
Formulas Used
Side of equilateral triangle = 2a
Height of equilateral triangle = (√3/2) * side
Circumcenter of equilateral triangle = Centroid
Centroid formula
(x-h)² + (y-k)² = r²
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📋 Question Details
- Chapter
- Coordinate Geometry
- Topic
- Circles
- Year
- 2013
- Shift
- 22 Apr Online
- Q Number
- Q76
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 11: Conic Sections
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