Deck 22: Analytic Geometry

Question 1

Find the distance between the points $(-35,81)$ and $(66,21)$ . Keep three significant digits.

Answer 1

117

Question 2

Find the distance between the given points: $(0,5)$ and $(1,-4)$

Answer 2

9.06

Question 3

Find the distance between the points $(-5.3,8.4)$ and $(9.2,-3.0)$ . Keep three significant digits.

Answer 3

18.4

Question 4

Find the distance between the points $(101,2)$ and $(807,-3)$ . Keep three significant digits.

Question 5

Find the distance between the points $(8,5)$ and $(-7,-4)$ . Keep three significant digits.

Question 6

Find the distance between the points $(b+2,5)$ and $(b-3,-2)$ . Keep three significant digits.

Question 7

Find the directed distance $A B$ if $A=(9,-1)$ and $B=(3,-1)$ .

Question 8

Find the directed distance $A B$ if $A=(5,-4)$ and $B=(7,-4)$ .

Question 9

Find the directed distance $A B: A(3.08,-2.37), B(-1.08,-2.37)$

Question 10

Find the directed distance $B A: A(10.55,4.35), B(-5.55,4.35)$

Question 11

Find the slope of the line passing through the points $(-5,-7)$ and $(3,-1)$ .

Question 12

Find the slope of the line passing through the points $(-4, b)$ and $(-b, 3)$ .

Question 13

Find the slope of the line passing through the points $(3, b-2)$ and $(5-b, 4)$ .

Question 14

Find the slope of the line having the given angle of inclination: $21.8^{\circ}$

Question 15

Find the slope of the line having the given angle of inclination: $143^{\circ}$ . Use three significant digits.

Question 16

Find the slope of a line having an angle of inclination of $0.957 \mathrm{rad}$ .

Question 17

Find the slope of a line having an angle of inclination of $0.625 \mathrm{rad}$ .

Question 18

Find the angle of inclination, in decimal degrees, of a line having a slope of $m=10$ .

Question 19

Find the angle of inclination, in decimal degrees, of a line having a slope of $m=-5.5$ .

Question 20

Find the slope of a line perpendicular to a line having a slope of $m=-4.80$ .

Question 21

Find the angle of inclination, in decimal degrees, of a line having the given slope: $m=-3.10$

Question 22

Find the angle of inclination, in decimal degrees, of a line having a slope of
$m=\frac{4}{7}$

Question 23

Find the angle of inclination, in radians, of a line having a slope of $m=-\frac{2}{3}$ .

Question 24

Find the slope of a line perpendicular to a line having an angle of inclination of $4.85 \mathrm{rad}$ .

Question 25

Find the slope of a line perpendicular to a line having an angle of inclination of $15 \overline{0}^{\circ}$ .

Question 26

Find the angle of inclination, in decimal degrees, of a line passing through the points $(8,-3)$ and $(5,6)$ .

Question 27

Find the angle of inclination, in decimal degrees, of a line passing through the points $(-5.2,5.4)$ and $(4.3,-3.5)$ .

Question 28

Find the angle of intersection between line 1 having an angle of inclination of $78^{\circ}$ and line 2 having an angle of inclination of $145^{\circ}$ .

Question 29

Find the angle of intersection between the line $y=4 x+5$ and the line $2 y-x=8$ . Use three significant digits.

Question 30

Find the angle of intersection between the line $y=\frac{3}{4} x-2$ and the line $y=-\frac{1}{3} x+1$ .

Question 31

Find the slope and $y$ -intercept for the equation $y=x+29$ .

Question 32

Find the slope and $y$ -intercept for the equation $y=-2$ .

Question 33

Write the equation, in slope-intercept form, of the line passing through the points $(-2,1)$ and $(3,-4)$ .

Question 34

Write the equation, in general form, of the line passing through the points $(-4,2)$ and $(6,-6)$ .

Question 35

Write the equation, in slope-intercept form, of the following line: $x$ -intercept $=-2 ; y$ -intercept $=4$ .

Question 36

Write the equation, in general form, of the line: slope $=1 / 4, y$ -intercept $=-3$

Question 37

Write the equation, in slope-intercept form, of the following line: $y$ -intercept $=-a$ ; slope $=2 b$

Question 38

Write the equation in general form, of the line passing through the point $(2,-3)$ and with a y-intercept of 1 .

Question 39

Determine the value of $a$ , so that the line $(a+2) x+\left(a^{2}-a\right) y+4 a^{2}+3 a-7=0$ passes through the origin.

Question 40

Determine the value of $a$ , so that the line $(a+2) x+\left(a^{2}-a\right) y+3 a^{2}-8 a+5=0$ is parallel to the $x$ -axis.

Question 41

Determine the value of $a$ , so that the line $(a+2) x+\left(a^{2}-a\right) y+3 a^{2}-8 a+5=0$ is parallel to the $y$ -axis.

Question 42

Write the equation, in slope-intercept form, of the following line: passes through $(-2,-1)$ ; parallel to $y=-1 / 2 x+3$

Question 43

Write the equation, in general form, of the line: passes through $(5,-1)$ and is parallel to $2 x-3 y=8$

Question 44

Write the equation, in slope-intercept form, of the line that passes through the point $(5,4)$ and perpendicular to the line $5 x-2 y-10=0$ .

Question 45

Write the equation, in general form, of the line: $y$ -intercept $=-1$ and perpendicular to $5 y-3 x=13$

Question 46

Write the equation, in general form, of the line: $y$ -intercept $=12$ and parallel to $4 x+5 y=8$

Question 47

Write the equation, in slope-intercept form, of the following line: passes through (-2.31, 4.05); angle of inclination $=135^{\circ}$

Question 48

Write the equation, in slope-intercept form, of line 1 in the graph below:

Question 49

Write the equation, in general form, of the line in the graph below:

Question 50

The highway regulations in a certain state say an interstate cannot rise more than $6.0 \mathrm{~m}$ for every $1 \overline{0} 0 \mathrm{~m}$ the road extends horizontally. What is the maximum angle of inclination a highway in this state can have?

Question 51

How long does a ramp need to be in order to meet the requirements of not to exceed a slope of 0.08 , if its height is $30 \mathrm{~cm}$ .

Question 52

A loading ramp has a rise of $2.3 \mathrm{~m}$ and a run of $8.1 \mathrm{~m}$ , what is the angle of inclination of the ramp?

Question 53

The angle of inclination of a set of stairs is $32.4^{\circ}$ . If the total rise of the stairs is $2.6 \mathrm{~m}$ , what is the total run of the stairs?

Question 54

A certain house has a roof with a $7 / 12$ pitch. In other words, the roof goes up 7 inches for every 12 inches across. What is the angle of inclination for the roof, to three significant digits?

Question 55

Using a ladder to reach the top of a $12-\mathrm{m}$ tall building, the ladder must not exceed an angle of $65^{\circ}$ with the ground to be safe. How far from the base of the building must the foot of the ladder be in order to be safe?

Question 56

Write the equation, in slope-intercept form, of the line that passes through the point $(-4,7)$ and perpendicular to the line $4 x-3 y+2=0$ .

Question 57

Write the equation of the circle in standard form: center at $(0,0)$ , radius $=4$

Question 58

Write the equation of the circle in standard form: center at $(2,5)$ , radius $=3$

Question 59

Write the equation of the circle in general form: center at $(4,-7)$ , passes through $(1,-3)$

Question 60

Write the equation of the circle in general form with a radius $r=5$ if the line $x-2 y-1=0$ is a tangent to this circle at point $(3,1)$ .

Question 61

Write the equation of the circle $(x-4)^{2}+(y+3)^{2}=9$ in general form.

Question 62

Write the equation of the circle $x^{2}+y^{2}+2 x-6 y+6=0$ in standard form.

Question 63

Find the center and radius of the circle: $x^{2}+y^{2}=64$

Question 64

Find the center and radius of the circle: $x^{2}+y^{2}-18 y=-17$

Question 65

Write the equation of the tangent to the circle at the given point: $(x-3)^{2}+(y+2)^{2}=100$ at $(-3,6)$

Question 66

Write the equation of the tangent to the circle at the given point: $(x-3)^{2}+(y+5)^{2}=25$ at $(0,-1)$

Question 67

Find the center and radius of the circle: $(x-8)^{2}+(y+5)^{2}=121$

Question 68

Find the center and radius of the circle: $x^{2}+y^{2}+10 x-4 y=52$

Question 69

Find the $x$ and $y$ intercepts for the circle: $x^{2}+y^{2}-6 x+8 y-11=0$ . Use three significant digits.

Question 70

Find the point(s) of intersection: $x^{2}+y^{2}-14 y-51=0$ and $x^{2}+y^{2}+20 x-36 y+399=0$

Question 71

Find the point(s) of intersection: $x^{2}+y^{2}+2 x-2 y-23=0$ and $x^{2}+y^{2}-6 x+12 y-35=0$

Question 72

Find the point(s) of intersection: $x^{2}+y^{2}-4 x+2 y-4=0$ and $x^{2}+y^{2}+2 x-4 y-11=0$

Question 73

Determine the coordinates of the points of intercepts of the circle $(x-4)^{2}+(y+3)^{2}=25$ with the coordinate axes.

Question 74

Determine the coordinates of the points of intercepts of the circle $(x-5)^{2}+(y-12)^{2}=169$ with the coordinate axes.

Question 75

Determine the equation of the tangent to the circle: $x^{2}+y^{2}=169$ at $(12,5)$

Question 76

Determine the equation of the tangents to the circle: $x^{2}-40 x+y^{2}=0$ at $(32,16)$

Question 77

Write the equation of the circle $(x-6)^{2}+(y+8)^{2}=144$ in general form.

Question 78

Write the equation of the circle $x^{2}+y^{2}-4 x-10 y+20=0$ in standard form.

Question 79

Find the focus and focal width of this parabola: $4 y^{2}+7 x=0$

Question 80

Find the focus and focal width of this parabola: $y^{2}=10 x$