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## High school geometry

### Course: High school geometry>Unit 7

Lesson 2: Standard equation of a circle

# Graphing a circle from its standard equation

Sal graphs the circle whose equation is (x+5)²+(y-5)²=4.

## Want to join the conversation?

• this corona stuff is hard becuase i have to do online school and its hard but im working my hardest can i get a shoutout.
• Keep up the good work! Hope that colleges/schools open again and stay open!
• at ,why did (x+5)^2 became (x- -5)^2 ? I'm doomedddd
• Sal wrote it that way to get it into the form of the equation for a circle, which is
(x - h)^2 + (y - k)^2 = r^2. In other words, the center of the circle is at (h,k), where h and k are the numbers being SUBTRACTED from x and y.
Hope this saves you from being doomedddd!
• this is not so clear to me yet so can anybody answer? how do you estimate how wide the circle is? i get that the radius is like the distance from the circle? so like in the first part of the video it is 4 points away from the center??
• The 4 in the video is the radius squared. You need to take the sqrt(4) = 2
This tells you the distance from the center of the circle to the edge (the radius) = 2.
Then, 2 * radius = the diameter of the circle (the total width). In this case it also happens to be 4.

Lets say the equation is: x^2 + y^2 = 25
From the equation we can tell:
1) The center of the circle is at (0, 0)
2) Sqrt(25) = 5. So, the radius of the circle = 5 (center of circle to the edge = 5). Thus, the diameter of the circle = 2*5 = 10 (entire width of the circle = 10)

Hope this helps.
• What makes the x plus 5 turn into x minus negative 5?
• The standard equation of a circle is (x-h)^2+(y-k)^2=r^2, where (h,k) is the center. The equation Sal started with was not in this format. Thus, in order to be able to graph the circle, he needed to change the appearance of the equation. We don't change the equation itself, though; we don't change any values.
Remember that a double negative equals a positive. In other words, two subtraction signs equals an addition sign. So that's what Sal did here, in order to put the equation in standard format. He merely changed how we see it.
Hope this helps!
• for the first one, how do we know it's negative five and not five? and same for the y, how do we know if it's positive or negative?
• The form of the equation is (x = h)^2 + (y -k)^2 = r^2, so you always have to change the sign of what is inside to find the point. This may not help, but I think of it as wanting to have the inside equal to 0 to see how much it moves, so if x - h = 0, then x = h.
• What will be the type of the triangle if 2 edges other than centre touches to the circle?Acute or Obtuse or Right angle triangle?
• If you always use the centre as one of the points, only 1 edge can touch the circle. After all, the other two edges must leave the circle to end up at the centre.
If all points are on the circle, then you can have any type of triangle. In fact, you can pick any random triangle at all, and you'll always be able to draw a circle around it such that the triangle's corner points (called "vertices") will all be on the circle.
• whats a center?
• The center of a circle is the point in the middle of the circle. All points that create the circle are an equal distance from that central point.
• so the equation of the circle can nor be represented by function?because for each x value we have two y valuse?
• Yes.you are right...
A function is a relation in which one variable specifies a single value of another variable. For example, when you toss a ball, each second that passes has one and only one ... We know that y is a function of x because for each x-coordinate there is ... can have more than one output (y-coordinate), and y is not a function of x
(1 vote)
• How do I find the center and radius of the equation
(x+2 radical sign 3)squared +(y +2 radical sign 3) squared = 1
• So, can I basically subtract either the `(h,k)` from the `(x,y)` or the `(x,y)` from the `(h,k)` as long as I'm consistent throughout the problem, since I will be squaring the answers?