Question

Find the centre and radius of the circle:

x²+y²-4x+6y+3=0

Answer 1

Answer:

Step-by-step explanation:

in an x–y Cartesian coordinate system,  

the circle with centre coordinates (a, b)  

and radius r  

is the set of all points (x, y)  

such that  

( x - a ) ² + ( y - b ) ² = r ²  

Let's now convert the given equation to this form;  

x ² + y ² - 4x - 6y + 3 = 0  

x ² - 4x + y ² - 6y = -3  

x ² - 4x + 4 + y ² - 6y + 9 = -3 + 4 + 9  

( x ² - 4x + 4 ) + ( y ² - 6y + 9 ) = 10  

( x - 2 ) ² + ( y - 3 ) ² = ( √10 ) ²  

coordinates of center is ( 2, 3 )  

radius of circle is √10 = 2.236  

Answer 2

Solution.........


If Have You Any Doubt Than You Can Ask me !!!

The given Equation is ------
${x}^{2} + \: {y}^{2} - 4x + 6y + 3 = 0$

Compare this equation with -----

${x}^{2} + {y}^{2} + 2gx + 2fy + c = 0$

So,

2g = - 4 and 2f = 6
g = -2 f = 3

and c = 3.

Now,

Centre = [ -g , -f ] = [ 2, -3 ]

and

radius =

$\sqrt{ {g}^{2} + {f}^{2} - c}$

$\sqrt{ {( - 2)}^{2} + {(3)}^{2} - 3} \\ \\ = \sqrt{4 + 9 - 3} \\ \\ \\ = \sqrt{13 - 3} \\ \\ \\ = \sqrt{10}$

$\\ \\ \\ hope \: this \: will \: help \: you \: ............ \\ \\ \\ \\ \\ \\ \\ \\ be \: brainly....................$

☛ ⛧⛧By, Ⓜr Thakur ⛧⛧