How do you find the standard form of #x^2 + y^2 + 8x + 2y - 8 = 0# and what kind of a conic is it?

1 Answer
Dec 7, 2015

Answer:

Shape: Circle
#(x+4)^2 + ( y+1)^2 = 9#

Explanation:

Remember: Some of the formula for conic are:
Circle: #(x-h)^2 + (y-k)^2 = r^2#
Ellipse: #(x-h)^2/a^2 + (y-k)^2/b^2 = 1#
Hyperbola:# (x-h)^2/a^2 - (y-k)^2/b^2 = 1#

Step 1: Complete the so to determine the form

#x^2 + 8x + y^2 +2y = 8#

#(x^2 + 8x+color(red)(16)) + (y^2 + 2y+color(red)(1)) = -8+ color(red)(16+ 1#

*Note: to complete the square, #color(red)(c= (b/2)^2#
#(x+4)^2 + ( y+1)^2 = 9#

Center: #(-4, -1)#
Radius: 3