Analytic Geometry Answers

Determine the equation of the hyperbola

Obtain the equation of the line with slope and passing through the point (-3, 4)

Determine \\(a-b-c\\), if \\(a=5i-2j\\), \\(b=3i+3j\\) and \\(c=4i-j\\)

Find in degrees the numeric value of the acute angle of rotation that eliminates the product term from the equation
7
x
2
+
24
x
y
−
34
x
+
24
y
−
185
=
0

Is there a sphere passing through (4,0,1),(10,-4,9),(-5,6,-11)and (1,2,3)?If so,find its equation.

Find the centre and radius of the sphere passing through (1,0,0),(0,1,0),(0,0,1) and (1/√3,1/√3,1/√3)?

If r = x
y
1
1 0 g
and A = 0 1 f
g f c
show that r^T Ar = 0 is the equation of the
circle in R^2 with centre (−g, −f) and radius square root(g^2 + f^2 − c).

Determine the sum of vectors \\(\\bar{CD}+\\bar{DA}\\)

If α=3i−j+2k, , β=2i+j−k and γÌ…=i−2j+2k, find α×β×γ.
a.24i+7j-5k
b.-24i+7j-5k
c.24i+7j+5k
d.24i-7j-5k

Given α=i+2j+3k, β=2i+j−k find α×β
a.5i+7j-3k
b.-5i+7j-3k
c.-5i+7j+3k
d.-5i-7j-3k