Geometry and TrigonometryHardTesting points against a circle's equation
Geometry and Trigonometry practice question
In the xy-plane, a circle has the equation (x + 3)² + (y − 1)² = 16. Which of the following points lies on the circle?
- A. (1, 1)Correct
- B. (−3, 1)
- C. (0, 0)
- D. (1, 5)
Answer: A. (1, 1)
Substitute (1, 1): (1 + 3)² + (1 − 1)² = 16 + 0 = 16. It satisfies the equation, so it lies on the circle. (It is 4 units to the right of the centre (−3, 1).)
Why the other answers are wrong
- B. (−3, 1)
- (−3, 1) is the CENTRE, giving 0 + 0 = 0, not 16.
- C. (0, 0)
- (0, 0) gives 9 + 1 = 10, not 16.
- D. (1, 5)
- (1, 5) gives 16 + 16 = 32, not 16.
More Geometry and Trigonometry questions
- Hard
In a right triangle, one leg is 5 and the hypotenuse is 13. What is the length of the other leg? - Hard
A circle has a radius of 4. What is the length of an arc that subtends a central angle of 90°? - Hard
A circle is defined by the equation (x − 3)² + (y + 2)² = 25. What is the radius of the circle? - Hard
What is 135° expressed in radians? - Hard
What is the length of segment PT? - Hard
What is the measure, in degrees, of the central angle of this sector?
Not affiliated with the College Board. SAT is a trademark of the College Board.