Question

Find the centre and radius of the
equation given below

(1) x2 + y2 - 4x -8y-41 = 0​

Answer 1

Answer:

EQUATION OF A CIRCLE

The equation of a circle comes in two forms:

1) The standard form: (x - h)2 + (y-k)2 = r2

2) The general form : x2 + y2 + Dx + Ey + F = 0, where D, E, F are constants.

If the equation of a circle is in the standard form, we can easily identify the center of the circle, (h, k), and the radius, r . Note: The radius, r, is always positive.

Example 1: (x-2)2 + (y-3)2 = 4. (a) Find the center and radius of the circle. (b) Graph the circle.

Note: A common mistake is to take h= -2 and K= -3. In an equation, if the sign preceding h and k , ( h, k) are negative, then h and k are positive. That is, h= 2 and k= 3.

(a) Center: (h= 2, k= 3) = ( 2, 3 ) and radius r=2 since r2 = 4 => r = Ö4 = 2

(b) The graph is