Analytic Geometry Answers

Find the equation of the line which passes through the point (9,5

9,5) and has slope 1

1. Give your answer in the form y=m x+b

y=m x+b. The constants should be given exactly, e.g., 1/3 rather than 0.33.

For what values of c are the vectors [−8, 𝑐, 4] and [𝑐, 𝑐 2 , 𝑐] orthogonal?

Find the equation of the ellipse in standard form whose Foci is (2,7) and (-2,7) and the length of the major axis is 6

5. Find the angle from the line 2x + y – 8 = 0 to the line x + 3y + 4 = 0. Draw the lines and

locate the angle formed.

6. Two sides of a square lie along the lines 2y = 20 – 3x and 3x + 2y = 48. Find the area of

the square.

3. Find the equation of the line parallel to 5x + 6y – 10 = 0 at a distance 61 from (-3,7).

4. Find the equation of the line parallel to 3x + 4y = 20 and at a distance of 5 units from this

line.

The line through the point (1,0,6) and perpendicular to the plane "x+3y+z=5" has vector equation "\\mathbf{r}=( u,v,w )=( a,b,c )+ t (d,e,f )" where t is a parameter.

Making use of the parameter t, find the values of: u; v and w

You are given the line "l:\\mathbf{r}=(1+2\\lambda,-1-\\lambda,3\\lambda)" , where "\\lambda" is a parameter.

Which of the following statements are true?

1. The point (3,-2,3) lies on the line "l"
2. The vector (2,−1,3) is parallel to the line.
3. Line "l" is perpendicular to the line "\\mathbf{r}=(2t, 2-t,-1+3t)" , where "t" is a parameter.
4. The equation of a plane containing line "l" and also passing through the point "(0,2,\u22121)" is "8x+y-5z=7" .
5. The vector "(2,\u22121,3)" is perpendicular to the line "l" .

You are given the following three points A(1,−3,5), B(4,-11,1) and C(-3,8,5).

Which of the following statements are true?

1. The vector equation of the line AB is "\\mathbf{r}=(1,-3,5)+\\lambda (3,-8,-4)" , where "\\lambda" is a parameter.
2. The three points  A, B  and C ie on the same straight line
3. "\\underline{AB} \\times \\underline{AC}=(44,16,1)"
4. Lines AB and AC are perpendicular.
5. The equation of a plane passing through the points A, B and C is "44x+16y+z=1"

Find the equation of the locus of a point so that the square of its distance from (3, -3) is always numerically equal to the slope of the line joining it to the same point.