What Are the Steps to Solve These Circle and Slope Math Problems?

In summary: So, the general form is x^2+y^2+4x-2y-20=0. Now, we can make it into the standard form! We can do it in one step, but I'm going to do it in 2 steps. Step 1: Factor x^2+4x, and y^2-2y, and leave the -20 alone. x^2+4x=(x+2)^2-4, and y^2-2y=(y-1)^2-1. Now, we have (x+2)^2+(y-1)^2-4-1-20=0. Simplify and we get
  • #1
alliecr
11
0
1.) How do you answer this?
Find the equation of the line that has a slope undefined and passes through the points (3, -4).

I got y=-4
------------------------
2.) Write the standard and general equations of the circle with radius 4 and center (1,2).
I got STANDARD: (x-1)^2 + (y-2)^2=16
I don't understand the whole GENERAL FORM!
------------------------
3.) Then I have this: Give the center, radius, and all intercepts of the circle: x^2+y^2+4x-2y-20=0.
I am stuck on this one completely.

Thank you for all help!
 
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  • #2
1. What is the point-slope equation?

2. Correct.

3. Complete the square, put it in general form, which C(h,k) is the center.

General form just basically tells us where the center is, and the length of the radius. If I were to ask you the difference between [tex]y=x-1[/tex] & [tex]y=x+1[/tex]. You would say the first is shifted a unit down, while the 2nd is shifted up a unit. Same thing for the circle. For example: [tex](x-1)^2+(y-2)^2=4[/tex], shifted to the right 1 & up 2 with radius 2.
 
Last edited:
  • #3
#1: You want a slope undefined. Your answer is a slope of zero. They are not the same.

#2: You obtained the correct equation in standard form, but you want the final answer in GENERAL form. Perform the steps (meaning, multiply!)
 
  • #4
symbolipoint said:
#1: You want a slope undefined. Your answer is a slope of zero. They are not the same.

#2: You obtained the correct equation in standard form, but you want the final answer in GENERAL form. Perform the steps (meaning, multiply!)
Crap! Sorry, I'm a dummy. General form is what they have in question 3. Standard form is C(h,k) form, hehe.
 

Related to What Are the Steps to Solve These Circle and Slope Math Problems?

1. What is the formula for finding the circumference of a circle?

The formula for finding the circumference of a circle is C = 2πr, where C represents the circumference and r represents the radius of the circle.

2. How do I find the slope of a line?

The slope of a line can be found by using the formula m = (y2 - y1) / (x2 - x1), where m represents the slope and (x1, y1) and (x2, y2) represent any two points on the line.

3. Can I find the equation of a line using only the slope and a point?

Yes, you can find the equation of a line using the slope and a point by using the point-slope form of the equation: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.

4. How do I graph a circle on a coordinate plane?

To graph a circle on a coordinate plane, you will need to know the coordinates of the center of the circle and the length of the radius. Plot the center point on the coordinate plane and use the radius to draw the circle around it.

5. Is there a difference between the radius and the diameter of a circle?

Yes, the radius and diameter of a circle are two different measurements. The radius is the distance from the center of the circle to any point on the circle's edge, while the diameter is the distance across the circle passing through the center.

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