Advertisement Remove all ads

Find the centre and radius of the following: 4x2 + 4y2 − 24x − 8y − 24 = 0 - Mathematics and Statistics

Sum

Find the centre and radius of the following:

4x2 + 4y2 − 24x − 8y − 24 = 0

Advertisement Remove all ads

Solution

The given equation, after dividing it by 4, can be written as:

x2 + y2 − 6x − 2y − 6 = 0

Comparing it with the equation

x2 + y2 + 2gx + 2fy + c = 0, we get,

2g = − 6, 2f = − 2 and c = − 6

∴ g = − 3, f = − 1 and c = − 6

∴ centre of the circle = ( − g, − f) = (3, 1)

and radius of the circle = `sqrt("g"^2 + "f"^2 - "c")`

= `sqrt((-3)^2 + (-1)^2 - (-6))`

= `sqrt(9 + 1 + 6)`

= 4.

  Is there an error in this question or solution?
Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×