Analytic Geometry Answers

1. Solve for the area in square units of the right triangle with vertices F(0,7),U(2,-3),N(7,-2)

2. Find the area in square units of a rectangle whose vertices are L(0,6),O(2,-2),V(-2,-3),E(-4,5)

what is the equation of a circle passing through (6,2) and tangent to the line x-4y-15=0 at (3,-3)

Find the equation of a line that passes through the point (2,1) and has a gradient of 2.

Leave your answer in the form y

=

m

x

+

c

With respect to the bar of chocolate, where is their center of mass?

The initial x-coordinates of James and Ramon are -10.0 m and +10.0 m respectively,

so the x-coordinate of the center of mass is:

Formula:

Solution:

Final Answer

Change the following point from rectangular to polar coordinate

‐ Square root of 3,2

Ii.change the following point from polar to rectangular coordinate

(3/2, n/12)

Find the equation of a line that passes through the point (2,1) and has a gradient of

−

1

3

.

Leave your answer in the form

y

=

m

x

+

c

Plot the following points:

P1 (-3, 135°)

P2 (2, )

P3 (4, 405°)

Graph

Sketch the graph of r = 3 − 2cosθ.

Find the radius and centre of the circular section of sphere |r|= 4, cut off by the plane

r.(2i-j+4k)= 3.

1. Convert the polar coordinates (-8, 2π/3) into rectangular coordinates.
2. Convert the rectangular coordinates (3, -3) into polar coordinates with r > 0 and 0 ≤ θ < 2π.
3. Convert the rectangular equation x2 + y2 = 100 into a polar equation that expresses r in terms of θ.
4. Convert the polar equation 4r cos θ + r sin θ = 8 into a rectangular equation that expresses y in terms of x.

Exercise 6.1

Plot the following points:

1.P1 (-3, 135°)

P2 (2, -3.14/3)

P3 (4, 405°)

   Then graph

2.Sketch the graph of r = 3 − 2cosθ.