College math
posted by Angel on .
Analyze x²6x5y=1. Determine the vertex, focus, directrix, intercepts, axis of symmetry, and at least 2 other points on the graph.

X^2  6X  5Y = 1.
Solve for Y:
5Y = X^2 + 6X +1,
Divide both sides by 5:
Eq2: Y = X^2/5  6X/5 + 1/5,
h = Xv = b/2a = (6/5) / (2/5) = 3.
Substitute 3 for X in Eq2:
k = Yv = 3^2/5  6*3/5 + 1/5,
k = 9/5  18/5 + 1/5,
k = 9/5  17/5 =  8/5 = 1 3/5.
V(h , k) = V(3 ,  1 3/5 )
Axis = h = 3.
F(3 , Y2)
V(3 ,  1 3/5)
D(3 , Y1)
4a = 4(1/5) = 4/5.
1/4a = 5/4 = 1 1/4.
Y2 = K + 1/4a,
Y2 =  8/5 + 5/4,
Common denominator = 20:
Y2 =  32/20 + 25/20 =  7/20.
Y1 = K  1/4a,
Y1 =  8/5  5/4,
Y1 = 8/5  5/4,
Common denominator = 20:
Y1 = 32/20  25/20,
Y1 = 57/20 = 2 17/20.
F(3 , 7/20)
V(3 , 1 3/5)
D(3 , 2 17/20)
P1(2 , 1 2/5)
P2(4 , 1 2/5)
XIntercepts = 5.8 , 0.17.
Use Quadratic Formula. 
CORRECTION: The constant in Eq2 should
be NEGATIVE 1/5.
Y = X^2/5  6X/5  1/5,
h = Xv = b/2a = (6/5) / (2/5) = 3.
Substitute 3 for x in Eq2:
k=Yv=3^2/5  6*3/5  1/5 =  10/5 =2.
V(h , k) = V(3 , 2).
Axis = h = 3.
4a = 4(1/5 = 4/5).
1/4a = 5/4 = 1 1/4.
F(3 , Y2)
V(3 , 2)
D(3 , Y1)
Y2 = K + 1/4a = 2 + 5/4 = 3/4.
Y1=K1/4a = 2  5/4 = 13/4 = 3 1/4.
F(3 , 3/4)
V(3 , 2)
D(3 , 3 3/4)
P1(2 , 1 4/5)
P2(4 , 1 4/5)
XIntercepts = 6.16 and 0.16.