Analytic Geometry Answers

If l, m be the portions of the axes of x and y intercepted by the tangent at any point ( x,y) on the curve ( x/a )^2/3+  (  y/b)^2/3  , show that ( l^2/a^2) +(m^2/b^2)=1

If A is the point (−3, 5, 10) and B is the point (12, −5, −15), find the coordinates of point P on the line AB given that AP: PB = 2: 3.

𝑥2 + 𝑦2 − 8𝑥 + 2𝑦 − 32 = 0?

If A is the point (−3, 5, 10) and B is the point (12, −5, −15), find the coordinates of point P on the line AB given that AP: PB = 2: 3.

write the equation of the line that passes through the points (2,1,3) and (1,4,-3). write all three forms of the equations of the line.

Definition, Formula and Physical interpretation of Cross Product.

1). Given the following vectors: u=(1, 2, -4) and v=(2, 3, 5)

Find:

a) u.v

b) u.u

c) (u.v) v

d) angle between u and v

e) unit vector

2. )Suppose that B =(2, 2, 1) and makes 30° with A and A•B = 6. What is the magnitude of A?

3. )What is the angle between A and B if A• B = 0

4.) Find (u+ v)•(2u – v) given that u•u= 4 u•v =-5 and v•v=10

5. )Determine if u and u = (cos 0, sin 0,–1); v=(sin 0,-cos 0,0) V are orthogonal

Definition, Formula and Physical interpretation of Collinear vector.

Definition, Formula and Physical interpretation of Cross Product.

A cable hangs in a parabolic arc between two poles 100 feet apart. The poles are 30 feet high and the lowest point on a suspended cable is 5 feet above the ground.

a) find the equation of the arc if the vertex is the lowest point of the cable

b) the opening of a cave 20 feet wide is in the shape of a semi ellipse. If the height of the opening is 15 feet at the center, how high is the opening 5 feet from the center.