Digital SAT Math : Circles - Practice Questions- New Syllabus
DSAT MAth Practice questions – all topics
- Geometry and Trigonometry Weightage: 15% Questions: 5-7
- Area and volume
- Lines, angles, and triangles
- Right triangles and trigonometry
- Circles
▶️Last Minutes DSAT Math revision Sheet
DSAT MAth and English – full syllabus practice tests
Question Foundation
In the xy-plane, a circle with radius 2 has center \((0,0)\). Which of the following is a equation of the circle?
A) \(x^2+y^2=2\)
B) \(x^2+y^2=4\)
C) \(x^2-y^2=2\)
D) \(x^2-y^2=4\)
▶️Answer/Explanation
Ans:B
The general equation of a circle with center \((h, k)\) and radius \(r\) is:
\[
(x – h)^2 + (y – k)^2 = r^2
\]
Center \((0,0)\)
Radius \(2\)
Substitute these values into the equation:
\[
(x – 0)^2 + (y – 0)^2 = 2^2
\]
Simplify:
\[
x^2 + y^2 = 4
\]
▶️ Answer/Explanation
Ans: D
Complete the square: \( x^2 – 6x = (x – 3)^2 – 9 \)
\( y^2 – 8y = (y – 4)^2 – 16 \)
Equation becomes: \( (x – 3)^2 + (y – 4)^2 = 25 \)
Radius \( r = \sqrt{25} = 5 \)
Choice A: Incorrect, possibly \( \sqrt{4} \)
Choice B: Incorrect, possibly from coefficient \( \frac{6}{2} \)
Choice C: Incorrect, possibly \( \sqrt{16} \)
▶️ Answer/Explanation
Ans: A
\( \angle AOC = 90^\circ \), so arc \( \overline{AC} \) is \( \frac{90}{360} = \frac{1}{4} \) of circumference
Length \( \overline{AC} = \frac{1}{4} \times 36 = 9 \)
Choice B: Incorrect, \( \frac{1}{3} \) of circumference
Choice C: Incorrect, \( \frac{1}{2} \) of circumference
Choice D: Incorrect, full circumference