Question

Find the centre and
radius of a circle given by
the equation:
x2+y2-2x-4y-4=0​

Answer 1

Answer:

The equation of the circle given is : x² + y² - 2x - 4y - 4 = 0.

Now, we know that, the standard form of the equation of a circle is : (x - h)² + (y - k)² = r².

To get the equation given into standard form, We need to use complete the square method.

So, let us solve :

⇒ x² + y² - 2x - 4y - 4 = 0

⇒ x² - 2x + y² - 4y = 4

⇒ x² - 2x + (1)² + y² - 4y + (2)² = 4

⇒ (x - 1)² + (y - 2)² = (2)²

Here, we obtain the equation of circle in standard form.

Now when we compared the equations, We get to know that, h = 1, k = 2 and r = 2.

So, The centre of the circle = (1,2) and radius = 2 units.