PSAT Math : Arcs and Intercept
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Example Questions
Example Question #1 : How To Find The Equation Of A Circle
The endpoints of a diameter of circle A are located at points 
The formula for the area of a circle is given by A =πr2 . The problem gives us the endpoints of the diameter of the circle. Using the distance formula, we can find the length of the diameter. Then, because we know that the radius (r) is half the length of the diameter, we can find the length of r. Finally, we can use the formula A =πr2 to find the area.
The distance formula is 
The distance between the endpoints of the diameter of the circle is:
To find the radius, we divide d (the length of the diameter) by two.
Then we substitute the value of r into the formula for the area of a circle.
Example Question #231 : Coordinate Geometry
What is the equation for a circle of radius 9, centered at the intersection of the following two lines?
To begin, let us determine the point of intersection of these two lines by setting the equations equal to each other:
To find the y-coordinate, substitute into one of the equations. Let's use 
The center of our circle is therefore 
Now, recall that the general form for a circle with center at 
For our data, this means that our equation is:
Example Question #31 : Circles
A circle is centered on point 
The formula for a circle is
The area of a circle:
Therefore:
Example Question #233 : Coordinate Geometry
A circle with a radius of five is centered at the origin. A point on the circumference of the circle has an x-coordinate of two and a positive y-coordinate. What is the value of the y-coordinate?
Recall that the general form of the equation of a circle centered at the origin is:
x2 + y2 = r2
We know that the radius of our circle is five. Therefore, we know that the equation for our circle is:
x2 + y2 = 52
x2 + y2 = 25
Now, the question asks for the positive y-coordinate when x = 2. To solve this, simply plug in for x:
22 + y2 = 25
4 + y2 = 25
y2 = 21
y = ±√(21)
Since our answer will be positive, it must be √(21).
Example Question #1 : How To Find X Or Y Intercept
If the equation of a line is 4y – x = 48, at what point does that line cross the x-axis?
(–48,0)
(0,–48)
(0,–12)
(48,0)
(0,12)
(–48,0)
When the equation crosses the x-axis, y = 0. Plug 0 into the equation for y, and solve for x.
4(0) – x = 48, –x = 48, x = –48
Example Question #1 : How To Find X Or Y Intercept
Where does the graph of 2x + 3y = 15 cross the x-axis?
(7.5, 0)
(0, 0)
(0, 5)
(0, -5)
(-7.5, 0)
(7.5, 0)
To find the x-intercept, set y=0 and solve for x. This gives an answer of x = 7.5.
Example Question #1 : How To Find X Or Y Intercept
The slope of a line is equal to -3/4. If that line intersects the y-axis at (0,15), at what point does it intersect the x-axis?
60
20
5
-20
15
20
If the slope of the line m=-3/4, when y=15 and x=0, plug everything into the equation y=mx+b.
Solving for b:
15=(-3/4)*0 + b
b=15
y=-3/4x + 15
To get the x-axis intersect, plug in y=0 and solve for x.
0 = -3/4x + 15
3/4x = 15
3x = 15*4
x = 60/3 = 20
x=20
Example Question #2 : X And Y Intercept
If these three points are on a single line, what is the formula for the line?
(3,3)
(4,7)
(5,11)
y = 4x + 31
y = 4x - 9
y = 3x - 9
y = 5x + 11
y = 3x - 3
y = 4x - 9
Formula for a line: y = mx + b
First find slope from two of the points: (3,3) and (4,7)
m = slope = (y2 – y1) / x2 – x1) = (7-3) / (4-3) = 4 / 1 = 4
Solve for b by plugging m and one set of coordinates into the formula for a line:
y = mx + b
11 = 4 * 5 + b
11 = 20 + b
b = -9
y = 4x - 9
Example Question #1 : How To Find X Or Y Intercept
The slope of a line is 5/8 and the x-intercept is 16. Which of these points is on the line?
(0,10)
(16, 10)
(8,15)
(32,30)
(32,10)
(32,10)
y = mx + b
x intercept is 16 therefore one coordinate is (16,0)
0 = 5/8 * 16 + b
0 = 10 + b
b = -10
y = 5/8 x – 10
if x = 32
y = 5/8 * 32 – 10 = 20 – 10 = 10
Therefore (32,10)
Example Question #1 : How To Find X Or Y Intercept
A line has the equation: x+y=1.
What is the y-intercept?
0.5
-1
2
0
1
1
x+y=1 can be rearranged into: y=-x+1. Using the point-slope form, we can see that the y-intercept is 1.
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