3
QuizMultiple Choice

Conic Inequalities

Question 3 • Precalculus

Which properties describe the graph of (x + 5)2 + (y – 10)2 < 169?

Answer
A
circle with center at (–5, 10), shading inside the circle
B
circle with center at (5, –10), shading inside the circle
C
circle with center at (5, –10), shading outside the circle
D
circle with center at (–5, 10), shading outside the circle

Explanation

A circle inequality in the form (x − h)² + (y − k)² < r² has center (h, k), and the less-than sign means the region inside the circle. Here, (x + 5)² = (x − (−5))² and (y − 10)² give center (−5, 10), so the graph is a circle centered at (−5, 10) with shading inside.

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