What do you expect when you think of circle questions? Most students tend to think of questions related to area and circumference-perhaps rotational motion, if they're taken Physics. And while those questions certainly *can* show up on the SAT, they're far from the most common: they tend to show up less than one time per test.

So then, what *does* show up on the test? Questions related to the *graphs* of circles.

Test-takers tend to be much less prepared for this question type for a number of reasons. It's much more recent content; the graphs of circles first show up in Algebra 2. But a larger problem is has to deal with translation.

The graph of a circle with radius *r *and center (*h, k*) is shown above. Does anything about it stand out?

Astute students might notice that they're used to *k* being positive. For instance, Point-Slope Form for linear equations is usually written as:

*y *= *m*(*x *- *h*) + *k*

However, this is only appropriate when *x* and *y* are on the same side of the equation. A more precise understanding of translation can be gleaned by subtracting *k* from both sides:

(*y* - *k*)* *= *m*(*x *- *h*)

Here, we can see what really goes on with translation:

We've replaced

*x*with (*x - h*) to shift it right by*h*.We've replaced

*y*with (*y - k*) to shift it up by*k*.

And these rules remain consistent for every equation you'll encounter! Circles? Same rules. Parabolas? Identical. Trigonometric graphs? Easy. Even in three dimensions, if you replace *z* with (*z *- *l*), you'll shift it in the positive *z* direction by *l*.

However, there's just *one* circle question that's even more difficult than those above-and it shows up on about 50% of SATs. If you're shooting for above a 700 in the Math section, see if you can figure it out!

If you think you know why B is the correct choice, leave a comment below and see if you're right or not!

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