Respuesta :
The equation of the circle having point (4,-17) and the center (-4,-2) is [tex]x^{2} +y^{2} +8x+4y-269=0[/tex].
Given a point on circle (4,-17) and the center of the circle be (-4,-2).
We are required to find the equation of the circke with center (-4,-2) containing the point (4,-17).
Equation is basically the relationship between two or more variables that are expressed in equal to form.
Equation of the circle is [tex](x-h)^{2} +(y-k)^{2} =r^{2}[/tex] in which (h,k)is point and r is radius.
We have to calculate the radius of the circle.
r=[tex]\sqrt{(4+4)^{2}+(-17+2)^{2} }[/tex]
=[tex]\sqrt{64+225}[/tex]
=[tex]\sqrt{289}[/tex]
=17
The equation will be [tex](x+4)^{2} +(y+2)^{2} =17^{2}[/tex]
[tex]x^{2} +16+8x+y^{2} +4+4y=289[/tex]
[tex]x^{2} +y^{2} +8x+4y-269=0[/tex]
Hence the equation of the circle having point (4,-17) and the center (-4,-2) is [tex]x^{2} +y^{2} +8x+4y-269=0[/tex].
Learn more about equation at https://brainly.com/question/2972832
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