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What are the curve and line coordinates for x square plus y square plus 4x plus 6y - 40 equals 0 and x - y equals 10?
Wiki User
∙ 13y ago
I presume you want the points where the circle x2 + y2 + 4x + 6y - 40 = 0 and the line x - y = 10 meet.
x - y = 10
=> y = x - 10
Substitute into circle equation:
x2 + y2 + 4x + 6y - 40 = 0
=> x2 + (x - 10)2 + 4x + 6(x - 10) - 40 = 0
=> x2 + x2 - 20x + 100 + 4x + 6x - 60 - 40 = 0
=> 2x2 - 10x = 0
=> 2x(x - 5) = 0
=> x = 0 or 5
=> y = -10 or -5 respectively
The line meets the circle at the points (0, -10) and (5, -5).
Another method with the same result:
Equation 1: x2+y2+4x+6y-40 = 0
Equation 2: x-y = 10 => x = 10+y
Substitute Equation 2 into Equation 1:
(10+y)(10+y)+y2+4(10+y)+6y-40 = 0
100+20y+y2+y2+40+4y+6y-40 = 0
Collect like terms:
2y2+30y+100 = 0 => (2y+20)(y+5) = 0
y = -10 or y = -5
Substitute the above values into Equation 2:
When y = -10, x = 0
When y = -5, x = 5
Therefore the coordinates are: (0,-1) and (5,-5)
Wiki User
∙ 13y ago
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