Question

the center and radius of the circle given by x2+y2-4x-5=0​

Answer 1

SOLUTION :-

TO DETERMINE :-

The center and radius of the circle given by

$\sf{ {x}^{2} + {y}^{2} - 4x - 5 = 0 }$

FORMULA TO BE IMPLEMENTED :-

For the circle of the form

$\sf{ {(x - a)}^{2} + {(y - b)}^{2} = {r}^{2} }$

The center of the circle is ( a, b ) and

radius of the circle is r unit

EVALUATION :-

Here the given equation of the circle is

$\sf{ {x}^{2} + {y}^{2} - 4x - 5 = 0 }$

Which can be rewritten as below

$\sf{ {x}^{2} - 4x + 4+ {y}^{2} - 9= 0 }$

$\implies \: \sf{ {x}^{2} - 2.2.x + {(2)}^{2} + {y}^{2} = 9 }$

$\implies \: \sf{ {(x - 2)}^{2} + {(y - 0)}^{2} = {(3)}^{2} }$

Which is of the form

$\sf{ {(x - a)}^{2} + {(y - b)}^{2} = {r}^{2} }$

Hence the required center of the circle is ( 2, 0) and radius of the circle is 3 unit

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. Find the equation of straight line passing through the point (-4,5) and making equal intercepts on the coordinate axis.

https://brainly.in/question/25257443

2. Locate the following points on the cartesian plane(aEr) (0,a),(a,0),(-a, 0),(0,-a)

https://brainly.in/question/26822338