Question

4x^+5y^-100=0 Найдите центральные координаты и радиус?

Answer 1

Перепишем его как: 4x^2+5y^2=100; В общем виде это (X-xO)^2+(y-y0)^2=r^2 => радиус равен корень из 100=10 Центр координаты:по иксу=0 По игрэку=0

Answer 2

Finding the Central Coordinates and Radius

To find the central coordinates and radius of the given equation 4x^2 + 5y^2 - 100 = 0, we can first rewrite the equation in the standard form of a circle equation, which is given by:

x^2 + y^2 + 2gx + 2fy + c = 0

Where the center of the circle is given by (-g, -f) and the radius is given by sqrt(g^2 + f^2 - c).

Rewriting the Equation

By completing the square for both x and y, we can rewrite the equation in the standard form.

For x: 4x^2 - 100 = -5y^2 4x^2 = 5y^2 + 100 x^2 = (5y^2 + 100)/4

For y: 5y^2 + 100 = 4x^2 5y^2 = 4x^2 - 100 y^2 = (4x^2 - 100)/5

Identifying the Coefficients

Comparing the rewritten equations with the standard form, we can identify the coefficients: g = 0 f = 0 c = -100

Finding the Center and Radius

The center of the circle is given by (-g, -f), which in this case is (0, 0).

The radius of the circle is given by sqrt(g^2 + f^2 - c), which in this case is sqrt(0^2 + 0^2 - (-100)) = sqrt(100) = 10.

Therefore, the central coordinates of the circle are (0, 0) and the radius is 10.