Question

Certain circle can be represented by the following equation. x^2+y^2+18x+14y+105=0x 2 +y 2 +18x+14y+105=0x, squared, plus, y, squared, plus, 18, x, plus, 14, y, plus, 105, equals, 0 what is the center of this circle ?

Answer 1

GIVEN :

The circle can be represented by the following equation $x^2+y^2+18x+14y+105=0$

TO FIND :

The centre of the given circle.

SOLUTION :

Given circle equation is $x^2+y^2+18x+14y+105=0\hfill (1)$

The general form of the circle equation is given by

$x^2+y^2+2gx+2fy+c=0\hfill (2)$

Comparing the equations (1) and (2)

Equating 2g=18 and 2f=14

2g=18

$g=\frac{18}{2}$

∴ g=9

2f=14

$f=\frac{14}{2}$

∴ f=7

The formula for centre of the circle is (-g,-f)

Now substitute the values of g and f we get,

Centre=(-9,-7)

∴ the centre for the given circle is (-9,-7)