A circle, C, has an equation: x^2 + y^2 - 4x + 10y = 7 . Find the centre of the circle and its radius?
The equation given needs to be transformed into a more familiar equation of a circle which we know the properties of and are therefore able to find its centre. Do you know what type of equation im speaking of?Thats right, its this equation of a circle that goes like (x-a)2 + (y-b)2 = r2 where the centre of the circle is (a,b) and the radius is r.We can get our original equation into this familiar form by factorising the equation into (x - 2) - 4 + (y + 5) - 25 = 7Therefore, the equation simplifies to (x - 2) + (y + 5) = 36 thus the circle has a centre at co-ordinates (2, -5) with a radius of 6.
