- The general equation of a circle is $$x^2+y^2+2gx+2fy+c=0$$. Here, the centre of the circle is (-g,-f); the radius of the circle is $$\sqrt{\ g^2+f^2-c}$$.
- Another form of equation for a circle is $$\left(x-a\right)^2+\left(y-b\right)^2=r^2$$ where (a,b) is the centre of the circle with radius "r" units.
- If the centre of the circle lies on the origin(0,0), the equation is $$\left(x-0\right)^2+\left(y-0\right)^2=r^2$$ ==> $$x^2+y^2=r^2$$, where r is the radius of the circle.
- For a triangle ABC, A (x1, y1), B (x2, y2), C (x3, y3):
- Centroid= $$\left(\frac{\left(x_1+x_2+x_3\right)}{3},\frac{y_1+y_2+y_3}{3}\right)$$
- Incentre= $$\left(\frac{\left(ax_1+bx_2+cx_3\right)}{a+b+c},\frac{ay_1+by_2+cy_3}{a+b+c}\right)$$; where a, b and c are the lengths of the BC, AC and AB respectively.
Coordinate Geometry - Circle and Triangle
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Coordinate Geometry - Circle and Triangle
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