x + y = -b/a

1

xy = c/a

(q,p)

(p,q)

2

q

p

\frac{-b}{2a}

d

d

3

4

5

xy = c/a

What if c/a is negative?

We'll use area to see 
if there is a solution

We'll use area to find d.

What's left is an area 
we have already calculated!

s = 8 (slider from -5 to 8, step 0.1)
csum: x + y = s
b = false
p = 8 (slider from 8 to 24, step 0.1)
hyp2: (x * y) = p
M = Intersect(csum, sym)
N = Intersect(hyp2, sym, 2)
hex, m, f, g, n, h, i = Polygon(M, (x(M), 0), (x(N), 0), N, (0, y(N)), (0, y(M)))
A = Intersect(hyp2, csum, 2)
B = Intersect(hyp2, csum, 1)
j = false
k = Segment(A, (x(A), 0))
l = Segment(M, (x(M), 0))
q = Segment(B, (x(B), 0))
o = false
r = false
t = Segment(M, (0, y(M)))
a_1 = Segment(B, (0, y(B)))
C = Intersect(k, t)
D = Intersect(l, a_1)
E = Intersect(sym, k)
poly2, c_1, m_1, d_1, e_1 = Polygon(C, M, D, E)
F = Intersect(t, yAxis)
G = Intersect(k, t)
H = Intersect(sym, k)
I = Intersect(a_1, yAxis)
poly3, f_1, g_1, h_1, i_1 = Polygon(F, G, H, I)
J = Intersect(sym, xAxis)
K = Point(q)
L = Point(l)
O = Intersect(l, a_1)
poly4, i_2, j_1, l_1, o_1 = Polygon(I, J, L, O)
u = false
v = 0 (slider from 0 to 1, step 0.01)
O' = Dilate(O, v, G)
L' = Dilate(L, v, F)
P = Point(k)
P' = Dilate(P, v, I)
poly5, h_2, p', l', o' = Polygon(H, P', L', O')
w = 0 (slider from 0 to 1, step 0.01)
poly6, b_1, k_1, n_1, p_1 = Polygon(L, O, H, P)
L'_1 = Dilate(L, w, P)
z = Vector(P, L'_1)
L'_2 = Translate(L, z)
O'_1 = Translate(O, z)
H' = Translate(H, z)
P'_1 = Translate(P, z)
poly6', l'_2, o'_1, h', p'_1 = Polygon(L'_2, O'_1, H', P'_1)
Q: (x(N), 0)
R: (x(B), 0)
a = 0 (slider from 0 to 1, step 0.01)
Q' = Dilate(Q, a, R)
poly1, q', c, d, e = Polygon(Q', (0, 0), (0, p / x(Q')), (x(Q'), p / x(Q')))
slides = 1 (slider from 1 to 14, step 1)
T = (0.8140407603318869, -1.834328103523326)
U = (9.437531628170799, -1.834328103523326)
S = (-0.6690439288211159, 1.2681138756611992)
V = (11.440798415386045, 1.2543102000026354)
W = (-0.6900564840586203, 1.2007500956350816)
Z = (3.076907554511998, 1.2007500956350816)
A_1 = (6.127745170098541, -0.07668965953910467)
B_1 = (11.303168425912492, -0.05011495732696636)
C_1 = (3.3579504808136256, 2.9664227519159962)
D_1 = (6.015420702027466, 2.9664227519159962)
u_1 = Vector(C_1, D_1)
E_1 = (-0.4992770901607848, 3.825258134944393)
F_1 = (11.356711113456186, 3.86962552731205)
G_1 = (0.7823589958975892, 4.093841852022836)
H_1 = (9.405849863736506, 4.093841852022836)
I_1 = (0.7737685689034319, 2.3462152725929557)
J_1 = (9.397259436742345, 2.3462152725929557)
K_1 = (-0.8453662352490996, -0.451414872218337)
L_1 = (11.836328866915547, -0.3846691085227355)
M_1 = (1.4289338610455355, 3.157800497988359)
N_1 = (10.42212982300256, 3.1160349543721617)
O_1 = (3.2088208929282924, 0.5374112566054157)
P_1 = (9.020349817251265, 0.5209287610705802)
Q_1 = (3.603510842248287, 2.690901520611002)
R_1 = (7.8640999744093785, 2.6616693481776488)
S_1 = (2.986335013942949, 0.4138079905024451)
T_1 = (7.260622478069895, 0.4217927614926946)
U_1 = (2.5684107406772343, -3.4635523051880357)
V_1 = (7.55980418367213, -3.463552305188036)
W_1 = (-0.25207055795484723, -0.32781160611536925)
Z_1 = (11.117476991913911, -0.3517782794127382)