Question 313004: x^2+6x+y^2-2y=90.....What is the conic section and identify the sections? What is the center points, vertices, foci, co-vertices, and directrix? what is the domain and range of each?
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! Start by setting this up to complete the square on the x and y terms.
x^2 + 6x +_____ +y^2 -2y+_____= 90 + _____ + _____
In order to complete the square, take HALF of the x and y coefficients, and SQUARE. Add this number to each side of the equation.
x^2 + 6x +9 + y^2 - 2y+ 1 = 90 +9 +1
(x+3)^2 +(y-1)^2 = 100
This is the equation of a circle, whose center is at (-3,1). The radius is 10.
Domain: x extends from -3, a distance of 10 in each direction. This would be from -3-10=-13 to -3 +10=7, including the endpoints. Domain is [-13,7].
Range: y extends from 1, a distance UP or DOWN 10 units. This is from 1-10 =-9 to 1+10=11, including the endpoints. Range is [-9,11].
Dr. Robert J. Rapalje, Retired
|
|
|
