[Video] Q9: (x-6)^2 + (y+5)^2 = 16 in the xy-plane, the graph of the equation above is a circle. point p is on the circle and has coordinates (10, −5). if pq is a diameter of the circle, what are the coordinates of point q ?

Explanation for Question 9 From the Math (No Calc) Section on the Official Sat Practice Test 8

So question number nine gives us an equation of a circle. 2 And then it tells us that point P on the circle has the coordinates 3 10 comment, negative five, and PQ is the diameter of the circle. 4 So which of the following coordinates are the coordinates of Q. 5 Right? And so first thing we need to know is what is the diameter 6 of the circle? And if we think back to the general equation, 7 the general form of the equation of a circle, 8 which I've written up here, we see that what comes after the equal sign 9 is the radius squared. And so 16 is equal to my radius squared, 10 my square root that I can see that forest, 11 my radius. That means that my diameter must be eight. 12 So whatever point I choose here in point P they should be eight units 13 away. And so a good way to do this is to draw a picture, 14 right? 15 And so I had point P at 10, common negative five. 16 So one, two, three, four, five, six, seven, eight, nine, ten one two, three, four, five. 17 So point P is right about here. 18 And now I can look at each of my answer choices and see are 19 we AOA? Now, if I look at a, 20 it says over two down five, 21 right? And so here I was at an X cohort of 10 and here 22 I was at an X coordinate of two. And so this used to work, 23 right? This is a distance of eight away. So it could be a possible 24 answer. Now, 25 if we think about PPP, 26 if we think about C right, 27 C is also down five, but instead it's over 1, 2, 3, 4, 5, 6. 28 And the difference between six, six and...