Explanation for Question 16 From the Math (Calc) Section on the 2019 October Sat
Not for number 16. We're told that we have a circle with a radius 2 of five and a center at negative eight, 3 comma six. And so we need to pick the pick the answer choice that 4 has the equation for the circle. So it's going to be useful to know 5 the general forum for an equation of circle. 6 And I would write this equation on a answer sheet or a, 7 a cheat sheet equation sheet, if you have one, 8 but it's going to be X minus H plus Y minus K. 9 And these are both squared is equal to the radius squared. 10 And so the first thing we can notice is that you should always have 11 the radius squared. It should never just be equal to the radius. 12 So since our radius is five, it has to be equal to five squared 13 and that's going to be 25. So we know it can't be C or 14 D because these both just have the normal radius. 15 And now the other important thing to notice here is that you have a 16 minus H and minus K and our center is always H comma 17 K. So essentially whatever signs you have on the center point, 18 they become flipped, right? Because X minus negative eight squared, 19 that's actually X plus eight squared, 20 right? And so that negative eight becomes a plus eight in the equation. 21 And then this plus six, right? That's Y minus six. 22 So this will become a negative that plus six becomes a negative six. 23 And so this equation that actually flips the signs like you're supposed to is 24 found here in the answer choice B a doesn't, 25 uh, put the signs in the right direction. It keeps the signs as you 26 see, as you see them here, but remember we want them to be the 27 opposite. And so that means that our best answer is going to be B.