x2 + y2 - 10x + 4y - 52 = 0
x2 - 10x + y2 + 4y = 52 Complete the square
(x2 - 10x + 25) + (y2 + 4y + 4) = 52 + 25 + 4
(x - 5)2 + (y + 2)2 = 81
(x - 5)2 + (y - -2)2 = 92
This is the equation of a circle with center (5, -2), and radius 9.
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The solutions work out as: x = 52/11, y = 101/11 and x = -2, y = -11
Straight line: 3x-y = 5 Curved parabola: 2x^2 +y^2 = 129 Points of intersection works out as: (52/11, 101/11) and (-2, -11)
y^(2) + 9y - 52 # Write down all the factors of '52' Hence 1, 52 ; 2 , 26 ; 4 , 13 ; By addition or subtraction, select a pair of factors that 'add' to '9' They are, '4' & '13' ; Hence 13 - 4 = 9 Set up ther brackets , without the signs Hence ( y 4)(y 13) Since '52' is negative (-) , then the two signs are different. Since '9' is positive then the larger factor is positive(+). Hence inserting (y - 4)(y + 13) Factored!!!! Done!!!!
-52x <= 7 (-52x)/(-52) >= 7/(-52) {divide both sides by -52, and reverse the inequality when dividing by a negative. x >= -7/52 There is no largest integer value for x. If the question was ... greater than or equal to ... then the solution would be x <= -7/52, and the largest integer value would be -1.
52