Question

Складіть рівняння кола, центр якого знаходиться в точці М(1; -3 ) і яке проходить через точку в (-2:5)

Answer 1

Ответ:

(х-1)²+(у+3)²=73

Объяснение:

R=√((-2-1)²)+(5+3)²)=

=√((-3)²+8²)=√(9+64)=

=√73

Формула рівняння кола:

(х-Хм)²+(у-Ум)²=R²; де Хм=1 абсциса центра кола; Ум=-3 ордината центра кола.

(х-1)²+(у+3)²=(√73)²

(х-1)²+(у+3)²=73

Answer 2

Equation of a Circle with Center and Point

To find the equation of a circle with a given center and a point that lies on the circle, we can use the formula:

(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 of the circle.

In this case, the center of the circle is given as M(1, -3) and the circle passes through the point (-2, 5).

Calculating the Radius

To calculate the radius of the circle, we can use the distance formula between the center of the circle (h, k) and the point on the circle (x, y):

r = sqrt((x - h)^2 + (y - k)^2)

Substituting the given values, we have:

r = sqrt((-2 - 1)^2 + (5 - (-3))^2) = sqrt((-3)^2 + (8)^2) = sqrt(9 + 64) = sqrt(73)

So, the radius of the circle is sqrt(73).

Equation of the Circle

Now that we have the center of the circle (1, -3) and the radius sqrt(73), we can substitute these values into the equation of a circle:

(x - 1)^2 + (y - (-3))^2 = (sqrt(73))^2

Simplifying the equation, we have:

(x - 1)^2 + (y + 3)^2 = 73

Therefore, the equation of the circle with center M(1, -3) and passing through the point (-2, 5) is (x - 1)^2 + (y + 3)^2 = 73.

I hope this helps! Let me know if you have any further questions.