SAT Circles Practice Question 12 (Hard)

Math · Geometry and TrigonometryHard

In the $xy$ -plane, the circle with equation $(x + 3)^2 + (y - 1)^2 = 26$ intersects the $x$ -axis at two points. What is the distance between these two points?

Student-produced response: enter your answer.

Show answer and explanation

Answer: 10

Points on the $x$ -axis have $y = 0$ . Substituting gives $(x + 3)^2 + 1 = 26$ , so $(x + 3)^2 = 25$ and $x + 3 = \pm 5$ . The intersection points are $(2, 0)$ and $(-8, 0)$ , which are $2 - (-8) = 10$ units apart.

Answering $5$ gives the distance from $x = -3$ to one intersection point, which is only half the chord.

Ask Owl about this question Next question

Got it wrong? On SAT Owl, Owl looks at the answer you chose and explains the exact mistake, then gives you similar questions until it sticks. Get your predicted SAT score free.