SAT Subject Test Mathematics Level 2

You’ll find circles, parabolas, ellipses, and hyperbolas on the Math 2 test. Like slope-intercept
questions, questions concerning circles and parabolas are essentially algebraic. Answering circles
questions like Example 5 is often just a matter of recalling and applying the appropriate equation.

CIRCLE

The equation    of  a   circle  centered    at  (h,k)   and with    radius  r   is:

(x  –   h)^2    +   (y  –   k)^2    =   r^2

Example 5

To use the formula for the equation of a circle, you need the coordinates (h,k) of the center. Here
they’re given: (2,–5). And you need the radius r. Here r = . So the equation is

(x  −   h)^2    +   (y  −   k)^2    =   r^2

(x  −   2)^2    +   (y  +   5)^2    =   3

The answer is (B).

Which   of  the following   equations   describes   the set of  all points  (x,y)   in  the coordinate  plane   that

are a   distance    of      from    the point   (2,−5)?

1.

(A) (x  −   2)^2    +   (y  −   5)^2    =   3

(B) (x  −   2)^2    +   (y  +   5)^2    =   3

(C) (x  +   2)^2    +   (y  +   5)^2    =   3

(D) (x  +   2)^2    −   (y  −   5)^2    =   3

(E) (x  −   2)^2    −   (y  +   5)^2    =   3