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A circle in the standard (x, y) coordinate plane is tangent to the x-axis at 4 and tangent to the y-axis at 4. Which of the following is an equation of the circle?
  • a)
    x2 + y2 = 4
  • b)
    x2 + y2 = 16
  • c)
    (x − 4)2 + (y − 4)2 = 4
  • d)
    (x − 4)2 + (y − 4)2 = 16
  • e)
    (x + 4)2 + (y + 4)2 = 16
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A circle in the standard (x, y) coordinate plane is tangent to the x-a...
The center of the circle is at (4,4), and the radius is 4. Therefore, the equation of the circle is (x-4)^2 + (y-4)^2 = 4^2. Expanding this equation, we get x^2 - 8x + 16 + y^2 - 8y + 16 = 16. Simplifying, we get x^2 + y^2 - 8x - 8y + 16 = 0. Therefore, the correct answer is (d) x^2 + y^2 - 8x - 8y + 16 = 0.
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A circle in the standard (x, y) coordinate plane is tangent to the x-a...
The correct answer is D. The best approach to this question is to draw a diagram as shown below:
The equation of a circle is (x − h)2 + (y − k )2 = r2. One way to find an equation for a circle is by using the coordinates of the center, (h, k ), and the radius, r. For this circle, the center is at (4, 4) and the radius is 4. Given center (4, 4) and radius 4, the circle has equation (x - 4)2 + (y - 4)2 = 42, or (x - 4)2 + (y - 4)2 = 16
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A circle in the standard (x, y) coordinate plane is tangent to the x-axis at 4 and tangent to the y-axis at 4. Which of the following is an equation of the circle?a)x2 + y2 = 4b)x2 + y2 = 16c)(x − 4)2 + (y − 4)2 = 4d)(x − 4)2 + (y − 4)2 = 16e)(x + 4)2 + (y + 4)2 = 16Correct answer is option 'D'. Can you explain this answer?
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A circle in the standard (x, y) coordinate plane is tangent to the x-axis at 4 and tangent to the y-axis at 4. Which of the following is an equation of the circle?a)x2 + y2 = 4b)x2 + y2 = 16c)(x − 4)2 + (y − 4)2 = 4d)(x − 4)2 + (y − 4)2 = 16e)(x + 4)2 + (y + 4)2 = 16Correct answer is option 'D'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about A circle in the standard (x, y) coordinate plane is tangent to the x-axis at 4 and tangent to the y-axis at 4. Which of the following is an equation of the circle?a)x2 + y2 = 4b)x2 + y2 = 16c)(x − 4)2 + (y − 4)2 = 4d)(x − 4)2 + (y − 4)2 = 16e)(x + 4)2 + (y + 4)2 = 16Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circle in the standard (x, y) coordinate plane is tangent to the x-axis at 4 and tangent to the y-axis at 4. Which of the following is an equation of the circle?a)x2 + y2 = 4b)x2 + y2 = 16c)(x − 4)2 + (y − 4)2 = 4d)(x − 4)2 + (y − 4)2 = 16e)(x + 4)2 + (y + 4)2 = 16Correct answer is option 'D'. Can you explain this answer?.
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