Uh Matematika (Menentukan Persamaan Dan Titik Pusat Serta Jari-jari Lingkaran)

Approved & Edited by ProProfs Editorial Team
The editorial team at ProProfs Quizzes consists of a select group of subject experts, trivia writers, and quiz masters who have authored over 10,000 quizzes taken by more than 100 million users. This team includes our in-house seasoned quiz moderators and subject matter experts. Our editorial experts, spread across the world, are rigorously trained using our comprehensive guidelines to ensure that you receive the highest quality quizzes.
Learn about Our Editorial Process
| By Frans_mat
F
Frans_mat
Community Contributor
Quizzes Created: 1 | Total Attempts: 2,278
Questions: 10 | Attempts: 2,278

SettingsSettingsSettings
Uh Matematika (Menentukan Persamaan Dan Titik Pusat Serta Jari-jari Lingkaran) - Quiz


Questions and Answers
  • 1. 

    Persamaan lingkaran dengan pusat (0,0) dan jari-jari 3 adalah...

    • A.

      X2 + y2 = 2

    • B.

      X2 + y2 = 4

    • C.

      X2 + y2 = 9

    • D.

      X2 + y2 = 16

    • E.

      X2 - y2 = 16

    Correct Answer
    C. X2 + y2 = 9
    Explanation
    The equation of a circle with center (0,0) and radius 3 is x^2 + y^2 = 9. This equation represents all the points (x,y) that are a distance of 3 units away from the origin (0,0). By substituting different values of x and y into the equation, we can verify that the equation holds true for all points on the circle. Therefore, x^2 + y^2 = 9 is the correct answer.

    Rate this question:

  • 2. 

    Jari-jari dan pusat lingkaran yang memiliki persamaan x2 + y2 + 4x − 6y − 12 = 0 adalah...

    • A.

      5 dan (−2, 3)

    • B.

      5 dan (2, −3)

    • C.

      6 dan (−3, 2)

    • D.

      6 dan (3, −2)

    • E.

      7 dan (4, 3)

    Correct Answer
    A. 5 dan (−2, 3)
    Explanation
    The equation of the circle is in the form (x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center of the circle and r is the radius. By comparing the given equation x^2 + y^2 + 4x - 6y - 12 = 0 with the standard form, we can see that the center of the circle is (-2, 3) and the radius is 5. Therefore, the correct answer is 5 and (-2, 3).

    Rate this question:

  • 3. 

    Persamaan lingkaran yang berpusat di (2,-3) dengan jari-jari 7 adalah...

    • A.

      X2 + y2 - 4x + 6y - 49 = 0

    • B.

      X2 + y2 + 4x - 6y - 49 = 0

    • C.

      X2 + y2 - 4x + 6y - 36 = 0

    • D.

      X2 + y2 + 4x - 6y - 36 = 0

    • E.

      X2 + y2 - 2x + 3y - 49 = 0

    Correct Answer
    C. X2 + y2 - 4x + 6y - 36 = 0
    Explanation
    The equation of a circle with center (h,k) and radius r is given by (x-h)^2 + (y-k)^2 = r^2. In this case, the center is (2,-3) and the radius is 7. Plugging these values into the equation, we get (x-2)^2 + (y+3)^2 = 7^2. Expanding this equation gives x^2 + y^2 - 4x + 6y - 36 = 0. Therefore, the correct answer is x^2 + y^2 - 4x + 6y - 36 = 0.

    Rate this question:

  • 4. 

    Jari - jari lingkaran x2 + y2 - 6x - 4y - 3 = 0 adalah...

    • A.

      4

    • B.

      5

    • C.

      6

    • D.

      7

    • E.

      8

    Correct Answer
    A. 4
    Explanation
    The given equation represents a circle in the form of (x - a)2 + (y - b)2 = r2, where (a, b) is the center of the circle and r is the radius. By comparing the given equation with the standard form, we can determine that the center of the circle is (3, 2) and the radius is √3. Since the question asks for the value of the radius, the correct answer is 4.

    Rate this question:

  • 5. 

    Pusat dan jari - jari lingkaran dari persamaan x2 + y2 - 4x + 12y - 9 = 0 adalah ...

    • A.

      (2,-6) dan 6

    • B.

      (-2,6) dan 6

    • C.

      (2,-6) dan 7

    • D.

      (-2,6) dan 7

    • E.

      (2,6) dan 7

    Correct Answer
    C. (2,-6) dan 7
    Explanation
    The given equation represents a circle in the coordinate plane. The general equation of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the coordinates of the center of the circle and r represents the radius. By comparing the given equation with the general equation, we can determine that the center of the circle is (2, -6) and the radius is 7. Therefore, the correct answer is (2, -6) dan 7.

    Rate this question:

  • 6. 

    Perhatikan gambar di bawah ini!

    • A.

      X2 + y2 = 25

    • B.

      X2 + y2 = 36

    • C.

      X2 + y2 = 49

    • D.

      X2 + y2 = 64

    • E.

      X2 + y2 = 81

    Correct Answer
    D. X2 + y2 = 64
    Explanation
    The given answer, x2 + y2 = 64, is correct because it follows the pattern of the other equations. Each equation represents a circle with a different radius. The equation x2 + y2 = 64 represents a circle with a radius of 8, which is the square root of 64. Therefore, it is the correct equation that fits the pattern of the other equations.

    Rate this question:

  • 7. 

    Persamaan lingkaran yang berpusat di (3,2) dan berjari - jari 4 adalah ...

    • A.

      X2 + y2 - 6x + 4y - 3 = 0

    • B.

      X2 + y2 - 6x - 4y - 3 = 0

    • C.

      X2 + y2 + 6x + 4y - 3 = 0

    • D.

      X2 + y2 - 4x - 6y - 3 = 0

    • E.

      X2 + y2 + 4x - 6y - 3 = 0

    Correct Answer
    A. X2 + y2 - 6x + 4y - 3 = 0
    Explanation
    The equation of a circle with center (h,k) and radius r is (x-h)^2 + (y-k)^2 = r^2. In this case, the center is (3,2) and the radius is 4. Plugging these values into the equation, we get (x-3)^2 + (y-2)^2 = 4^2, which simplifies to x^2 + y^2 - 6x + 4y - 3 = 0.

    Rate this question:

  • 8. 

    Diberikan persamaan lingkaran sebagai berikut: x2 + y2 −2x + 4y + 1 = 0. Jika pusat lingkaran adalah P(a,b) maka nilai dari 10a - 5b =...

    • A.

      -10

    • B.

      -5

    • C.

      5

    • D.

      10

    • E.

      20

    Correct Answer
    E. 20
    Explanation
    The equation of the circle can be rewritten as (x-1)² + (y+2)² = 4. Comparing this with the standard equation of a circle, (x-h)² + (y-k)² = r², we can see that the center of the circle is at point P(1, -2) and the radius is 2.

    To find the value of 10a - 5b, we can substitute the coordinates of the center into the expression.

    10a - 5b = 10(1) - 5(-2) = 10 + 10 = 20.

    Therefore, the correct answer is 20.

    Rate this question:

  • 9. 

    Persamaan lingkaran yang berpusat di P(3, – 4) dan menyinggung sumbu x adalah …

    • A.

      (x – 3)2 + (y – 4)2 = 9

    • B.

      (x – 3)2 + (y + 4)2 = 9

    • C.

      (x + 3)2 + (y – 4)2 = 9

    • D.

      (x + 3)2 + (y – 4)2 = 16

    • E.

      (x – 3)2 + (y + 4)2 = 16

    Correct Answer
    E. (x – 3)2 + (y + 4)2 = 16
    Explanation
    The given equation represents a circle centered at point P(3, -4) and touches the x-axis. The general equation of a circle is (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the center of the circle and r represents the radius. In this case, the center is (3, -4) and the radius is 4 (since 4^2 = 16). Therefore, the correct equation is (x - 3)^2 + (y + 4)^2 = 16.

    Rate this question:

  • 10. 

    Persamaan lingkaran pada gambar berikut adalah...

    • A.

      X2 + y2 = 5

    • B.

      X2 + y2 = 25

    • C.

      X2 - y2 = 5

    • D.

      X2 - y2 = 25

    • E.

      X2 + y2 = 10

    Correct Answer
    B. X2 + y2 = 25
    Explanation
    The equation x^2 + y^2 = 25 represents a circle with a radius of 5 units. This is because the equation of a circle centered at the origin is x^2 + y^2 = r^2, where r is the radius. In this case, r = 5, so the equation becomes x^2 + y^2 = 25.

    Rate this question:

Quiz Review Timeline +

Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.

  • Current Version
  • Mar 22, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Feb 06, 2017
    Quiz Created by
    Frans_mat
Back to Top Back to top
Advertisement
×

Wait!
Here's an interesting quiz for you.

We have other quizzes matching your interest.