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Question 692038: please help me solve these equations
label the endpoints of the axis
x^2/4+(y-1)^2/25=1
complete the square and write in standard form
x^2+y^2-10x-4y=9
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! label the endpoints of the major axis
x^2/4+(y-1)^2/25=1
This is an equation of an ellipse with vertical major axis
Its standard form: (x-h)^2/b^2+(y-k)^2/a^2=1, a>b, (h,k)=(x,y) coordinates of center
For given equation:
center: (0,1)
a^2=√25
a=√25=5
vertices: (endpoints of vertical major axis)=(0,1±a), ((),1±5)=(0-5) and (0,5)
...
complete the square and write in standard form
x^2-10x+y^2-4y=9
(x^2-10x+25)+(y^2-4y+4)=9+25+4
(x-5)^2+(y-2)^2=38
This is an equation of a circle with center at (5,2) and radius√38
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