What is the equation of a Circle with Origin as center and passing through the vertices of an equilateral triangle of altitude 3a.

Asked by Malavika Umesh | 30th Apr, 2015, 10:41: PM

Expert Answer:

Equation of any circle with center at origin and radius 'r' is 
x squared plus y squared equals r squared
If the altitude of an equilateral triangle is 3a, then its centroid/circumcenter will divide the altitude in 2:1 ratio and the longer part will be the radius of the circumcircle passing through the vertices. 
Hence, radius of the circle 'r' is 2a.
Hence, equation of the circle is 
x squared plus y squared equals open parentheses 2 a close parentheses squared rightwards double arrow x squared plus y squared equals 4 a squared

Answered by satyajit samal | 2nd May, 2015, 01:14: PM