How do you find the radius of a circle with the equation #x^2 - 8x + y^2 - 4y – 5 = 0#?
The equation of the circle in standard form is
25 is the square of the radius. So the radius must be 5 units. Also, the centre of the circle is (4, 2)
To calculate the radius/centre, we must first convert the equation to standard form.
where (h, k) is the centre and r is the radius of the circle.
The procedure to do this would be to complete the squares for x and y, and transpose the constants to the other side.
To complete the squares, take the coefficent of the term with degree one, divide it by 2 and then square it. Now add this number and subtract this number. Here, the coefficient of the terms with degree 1 for x and y are (-8) and (-4) respectively. Thus we must add and subtract 16 to complete the square of x as well as add and subtract 4 to complete the square of y.
Note that there are 2 polynomials of the form
Write them in the form of
This is of the standard form. So 25 must be the square of the radius. This means that the radius is 5 units.