Question

СРОЧНО ПОМОГИТЕ ПОЖАЛУЙСТА ДАЮ 35 БАЛЛОВСкладіть рівняння фігури, симетричної колу (x-7)^2+(y+3)^2 =8 відносно: а) початку координат; б) осі ОХ; в) осi OY; г)прямої у = х.​

Answer 1

Ответ:

Вот мне кажется что верно

Answer 2

Equation of a Symmetric Circle

To find the equations of the circle symmetric with respect to different axes and a given line, we can use the general equation of a circle and apply the appropriate transformations.

The general equation of a circle is given by: \( (x - h)^2 + (y - k)^2 = r^2 \) where (h, k) is the center of the circle and r is the radius.

Equation of the Circle Symmetric to the Origin (0,0)

The equation of the circle symmetric to the origin is obtained by replacing x with -x and y with -y in the general equation of a circle.

Given the equation of the circle: \( (x - 7)^2 + (y + 3)^2 = 8 \)

The equation of the circle symmetric to the origin is: \( (-x - 7)^2 + (-y + 3)^2 = 8 \)

Equation of the Circle Symmetric to the X-Axis

The equation of the circle symmetric to the x-axis is obtained by replacing y with -y in the general equation of a circle.

Given the equation of the circle: \( (x - 7)^2 + (y + 3)^2 = 8 \)

The equation of the circle symmetric to the x-axis is: \( (x - 7)^2 + (-y - 3)^2 = 8 \)

Equation of the Circle Symmetric to the Y-Axis

The equation of the circle symmetric to the y-axis is obtained by replacing x with -x in the general equation of a circle.

Given the equation of the circle: \( (x - 7)^2 + (y + 3)^2 = 8 \)

The equation of the circle symmetric to the y-axis is: \( (-x + 7)^2 + (y + 3)^2 = 8 \)

Equation of the Circle Symmetric to the Line y = x

The equation of the circle symmetric to the line y = x is obtained by replacing x with y and y with x in the general equation of a circle.

Given the equation of the circle: \( (x - 7)^2 + (y + 3)^2 = 8 \)

The equation of the circle symmetric to the line y = x is: \( (y - 7)^2 + (x + 3)^2 = 8 \)