Analytic Geometry Answers

QUESTION 8


8.1 Let L1 and L2 be lines defined by


x = w0 + su, s ∈ R


and y = w1 + tv, t ∈ R, respectively.


Show that L1and L2 are parallel if and only if u = kv for some k ∈ R.

(8)


8.2 Find the plane that passes through the point (2, 4, −3) and is parallel to


the plane −2x + 4y − 5z + 6 = 0.

(4)


8.3 Find the line that passes through the point (2, 5, 3) and is perpendicular to the plane


2x − 3y + 4z + 7 = 0.

(4)


8.4 Find an equation of the plane passing through the point(−2, 3, 4) and is

perpendicular to the line passing through the points (4, −2, 5) and (0, 2, 4).

(4)


[20]

What is the perimeter of △TUV?

Write your answer as an integer or as a decimal rounded to the nearest tenth.

Perimeter=

units

the coordinate points are T(-7,-9) V(3,10) U(6,-7)

A triangle has vertices A(-16,0) B(9,0) c(0,12).prove that the equation of the internal bisector of angle BAC of the triangle is x-3y+16=0

Let L1and L2 be the line defined by

x=wo+su and w1+tv

show that L1 and L2 are parallel if and only if u=if for some k €R

1) Let L1 and L2 be lines defined by :


x = w0 + su, s e R(element of R)

y= w1 + tv, t e R(element of R) respectively


Show that L1 and L2 are parallel if and only if u = kv for some k e R. (element of R)


2) Find the plane that passes through the point (2,4,-3) and is parallel to the plane - 2x + 4y - 5z + 6 = 0


3) Find the line that passes through the point (2,5,3) and is perpendicular to the plane 2x - 3y + 4z + 7 = 0


4) Find an equation of the plane passing through the point (-2,3,4) and is perpendicular to the line passing through the points (4,-2,5) and (0,2,4).

under what conditions are u + v and u − v orthogonal? Interpret your result geometrically

A triangle on a coordinate plane is translated to the rule T-3,-5(x,y). Which is another way to write this rule

Write an equation for the set of all points in the plane equidistant from (0, – 1) and y= – 5. Write your answer in vertex form. Simplify any fractions

Find the polar equations of the lines or curves whose Cartesian equations are

(a) (x x a)

2 + (y y a)

2 = a

2

(b) x

2/a2 + y

2/b2 = 1 (c) y = 2x (d) y = x

2

(e) xy = 4 (f) y = 4 (g) 3x x y + 2 = 0.

U= (-1,-7)

W= (3,1)

2U+(-3)w=