The circle with the equation x² + y²-4x-6 = 0 is translated by [2, -3]. The result is a circle centered on ...?

Sorry, I mean [2, -3] is a matrix with ordo (2x1)

1 Answer
Jim G.
Oct 29, 2017

#(4,-3)#

Explanation:

#"the standard form of the equation of a circle is"#

#color(red)(bar(ul(|color(white)(2/2)color(black)((x-a)^2+(y-b)^2=r^2)color(white)(2/2)|)))#

#"where "(a,b)" are the coordinates of the centre "#
#"and r is the radius"#

#"to obtain this form use the method of "color(blue)"completing the square"#

#x^2+2(-2)xcolor(red)(+4)+y^2=6color(red)(+4)#

#rArr(x-2)^2+y^2=10#

#"with (a,b)=(2,0)" and "r=sqrt10#

#"under a translation "((2),(-3))#

#"the centre of the circle will shift to"#

#(2,0)to(2+2,0-3)=(4,-3)#

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