The equation of the circle passing through the point (−5, −2) and center at (−2, 3) is [tex]\bold{( x +2 )^2 + ( y - 3 )^2 = 34}[/tex]
The general equation of the circle whose center at (h, k) and radius r is,
[tex]( x - h )^2 + ( y - k )^2 = r^2[/tex]
For given example,
the circle passing through the point (−5, −2) whose center is at (−2, 3).
The radius of the circle is the distance between point (-5, -2) and the center (-2, 3).
Using distance formula the radius of a circle would be,
⇒ [tex]r=\sqrt{(-2-3)^2 + (-5-(-2))^2}[/tex]
⇒ [tex]r=\sqrt{(-5)^2+(-3)^2}[/tex]
⇒ [tex]r=\sqrt{25+9}[/tex]
⇒ [tex]r=\sqrt{34}[/tex] units
Let center (h, k) = (-2, 3)
Using the general form of the circle,
⇒ [tex]( x - h )^2 + ( y - k )^2 = r^2[/tex]
⇒ [tex]( x - (-2) )^2 + ( y - 3 )^2 = (\sqrt{34})^2[/tex]
⇒ [tex]( x +2 )^2 + ( y - 3 )^2 = 34[/tex]
Therefore, the equation of the circle passing through the point (−5, −2) whose center is at (−2,3) would be [tex]\bold{( x +2 )^2 + ( y - 3 )^2 = 34}[/tex]
Learn more about the equation of the circle here:
https://brainly.com/question/13264501
#SPJ2
