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

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

x2 + y2 = 2

x2 + y2 = 4

x2 + y2 = 9

x2 + y2 = 16

x2 - y2 = 16

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.

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.

2. Perhatikan gambar di bawah ini!

x2 + y2 = 25

x2 + y2 = 36

x2 + y2 = 49

x2 + y2 = 64

x2 + y2 = 81

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.

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.

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

4

5

6

7

8

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.

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.

4. Persamaan lingkaran pada gambar berikut adalah...

x2 + y2 = 5

x2 + y2 = 25

x2 - y2 = 5

x2 - y2 = 25

x2 + y2 = 10

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.

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.

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

-10

-5

5

10

20

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.

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.

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

(2,-6) dan 6

(-2,6) dan 6

(2,-6) dan 7

(-2,6) dan 7

(2,6) dan 7

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.

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.

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

5 dan (−2, 3)

5 dan (2, −3)

6 dan (−3, 2)

6 dan (3, −2)

7 dan (4, 3)

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).

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).

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

x2 + y2 - 4x + 6y - 49 = 0

x2 + y2 + 4x - 6y - 49 = 0

x2 + y2 - 4x + 6y - 36 = 0

x2 + y2 + 4x - 6y - 36 = 0

x2 + y2 - 2x + 3y - 49 = 0

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.

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.

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

(x – 3)2 + (y – 4)2 = 9

(x – 3)2 + (y + 4)2 = 9

(x + 3)2 + (y – 4)2 = 9

(x + 3)2 + (y – 4)2 = 16

(x – 3)2 + (y + 4)2 = 16

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.

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.

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

x2 + y2 - 6x + 4y - 3 = 0

x2 + y2 - 6x - 4y - 3 = 0

x2 + y2 + 6x + 4y - 3 = 0

x2 + y2 - 4x - 6y - 3 = 0

x2 + y2 + 4x - 6y - 3 = 0

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.

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.