|
Question 1047164: Graph the given equation.
1) 25x^2 + y^2 - 100x + 6y + 84 = 0
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 25x^2 + y^2 - 100x + 6y + 84 = 0
rewrite, putting x and y together
25x^2-100x+y^2+6y=-84
25(x^2-4x)+y^2+6y+9=-84+9, complete the square of the y and also need to do x, after making the leading coefficient 1.
25(x^2-4x+4)+(y+3)^2=--84+9+100=25. Everything that is added to the left side must be added to the right.
25(x-2)^2+(y+3)^2=25
divide everything by 25
(x-2)^2+(y+3)^2/25=1. This is now the formula for an ellipse in standard form.
The center of this ELLIPSE is at (2,-3) with major axis boundaries at sqrt(25)=5 on the y-axis
(2,2) and (2,-8) and the minor axis at (1,-3) and (3,-3); the (x-2)^2/1 will have semi minor axis of length 1.
Can check in original equation.
(2.2):100+4-200+12+84
(2,-8): 100+64-200-48+84
(1,-3): 25+9-100-18+84
(3,-3): 225+9-300-18+84
|
|
|
| |
