Explanation for Question 20 From the Math (No Calc) Section on the 2019 April Sat
In number 20, we are given the equation for the graph of 2 a circle. We want to know if the circle is translating downward, 3 a unit such that the circle is tangent to the X axis. 4 What is the value of a, that makes the equation X minus X squared, 5 plus Y minus three, plus a squared is equal to 25. 6 So this is a little bit confusing to think about mentally. 7 So I'm going to make a picture. 8 So we start off with the circle that has this equation. 9 So I'm going to use that equation to find the center and the radius 10 of the circle. If you know the general equation of a circle, 11 that would be very helpful. And that is X minus 12 H squared. Plus Y minus K squared is 13 equal to R squared. This one is a very good one to memorize if 14 you haven't already. 15 So using this equation, the center happens at the point HK 16 and the radius is equal to R so you have to remember to take 17 the square root of R squared. 18 So now, if I look at this equation, 19 the center is at the 0.63. 20 Remember to take the opposite sign that that's what's inside because the original 21 equation has a minus side. And then the radius is 22 equal to five. 23 Since the square root of 25 is equal to five. 24 So now that I have that I can drop my first picture of this 25 circle, six three would be about here. 26 And then that means a circle would look something like 27 this. It just has to be a rough sketch. Nothing that'll take too much 28 time. So now we want to translate the circle, 29 downward ...