Analytic Geometry Answers

Find the midpoint of AB if A (-3,8) and B (-7,-6)

We consider two skew lines r and s in space, then

A.     For any point R of r and any point S of s the distance between R and S is constant.

B.     There is a single point R of r and a single point S of s such that the distance between R and S is minimal.

C.     There exist an infinite of points R in r and S in s such that the distance between R and S is minimal

D.     None of the above

The volume V of the parallelopiped that has u, v, w as adjacent edges is

given by: V = |u.(v × w)|. If u.(v × w) = 0, then u, v, w lie in the same

plane. Thus, find the volume of the parallelopiped formed by the followings:

u =< 1, 2, −1 >, v =< 2, −1, 2 >, w =< 2, −3, 4 >.

A triangle is formed by the lines y=x, y=2x-1 and 3y-4x=1. Find the area of the triangle

We consider two skew lines r and s in space, then

A.     For any point R of r and any point S of s the distance between R and S is constant.

B.     There is a single point R of r and a single point S of s such that the distance between R and S is minimal.

C.     There exist an infinite of points R in r and S in s such that the distance between R and S is minimal

D.     None of the above

A jet heads due west at 350 km/h. It experience a 100km/h crosswind flowing in the direction N60 degreesW.Find the speed of the jet?

Direction: Tell whether the equation represents a circle, parabola, ellipse or hyperbola.

1. 3x^2+6x-5y-7=0

The normal to the parabola y²= 4ax at the point P(at² , 2at) meets the x-axis at A. Find the equation of the locus of the midpoint of AP as t varies.

The coordinates of the ends of a focal chord of the parabola y²= 4ax are (x₁, y₁) and (x₂, y₂). Show that x₁x₂ = a² and y₁y₂ = −4a².

The tangents at the points P(ap² , 2ap) and Q(aq² , 2aq) on the parabola y²= 4ax intersect at the point R. Given that the tangent at P is perpendicular to the chord OQ, where O is the origin, find the equation of the locus of R as p varies.