The equation of a circle whose centre ([tex]-5,-2[/tex]) and radius [tex]2[/tex] is [tex]x^{2}+y^{2}+10x+4y+25=0[/tex]
What is equation of a circle?
A circle is a closed curve drawn from a fixed point called centre of the circle. The distance between the centre of the circle and the arc of the circle is called the radius of the circle.
The equation of a circle with centre [tex](h, k)[/tex] radius [tex]r[/tex] is
[tex](x-h)^{2} +(y-k)^{2}=r^{2}[/tex]
Given center = [tex](-5,-2)[/tex] and Radius = [tex]2[/tex]
Put the Given value in the equation:
= [tex](x-(-5))^{2} +(y-(-2))^{2} = 2^{2}[/tex]
= [tex](x+5)^{2} +(y+2)^{2}=2^{2}[/tex]
= [tex](x^{2} +10x+25)+(y^{2}+4y+4)= 4[/tex]
= [tex]x^{2} +y^{2}+10x+ 4y+ 29 = 4[/tex]
= [tex]x^{2} +y^{2}+10x +4y+ 29-4=0[/tex]
= [tex]x^{2} +y^{2}+10x+4y+25=0[/tex]
So, the equation of the circle whose centre is [tex](-5,-2)[/tex] and Radius [tex]2[/tex] is
[tex]x^{2}+y^{2}+10x+4y+25=0[/tex]
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