Explanation for Question 11 From the Math (Calc) Section on the 2017 May Sat
For question 11, we want to write the equation of a circle that has 2 a sensor zero, zero, and radius four. 3 In order to do that, we need to know the formula for the equation 4 of a circle. The nice part is that we're not really applying it or 5 anything like that here. All we're doing is writing the equation. 6 So if you remember the formula for the equation of 7 a circle is X minus H squared, 8 plus Y minus K squared equals R squared. 9 A couple of important things here to remember these negative 10 signs or, or subtraction signs mean that your center is going to 11 be opposite as what it looks like. 12 So if your sensor for the, like the X value of the center is 13 five, you're going to have X minus five. 14 The next thing to remember is this square. 15 When the equation is equal to something, for example, 16 like here, it's equal to four, 17 that's not the radius, that's the radius squared. 18 So to find out what the radius is, you take the square root. 19 So now let's write our equation. Remember H M K R X and Y 20 values for the center, our squared or R is our radius. 21 And then we square in this case, 22 it was actually really simple because our center is zero, 23 zero. So we just plug in four H and 24 then K, and then we know the radius is four. 25 So we just plug in four for the radius. 26 And now we kind of simplify X minus zero is zero Y 27 minus zero . And remember we have to square the radius. 28 So four times four is 16 and that's our equation for 29 a circle or C.