Respuesta :
[tex]{(x-h)}^2 + {(y-k)}^2 = {r}^2[/tex] represent the equation of the new circle.
Given: (h,k) is center of circle
and (x,y) remains on edge of circle.
The distance formula is used to determine the distance, d, between two points. If the coordinates of the two points are (x1, y1) and (x2, y2), the distance equals the square root of x2 − x1 squared + y2 − y1 squared.
The distance formula is derived by creating a triangle and using the Pythagorean theorem to find the length of the hypotenuse. The hypotenuse of the triangle is the distance between the two points.
In a Cartesian grid, to measure a line segment that is either vertical or horizontal is simple enough. You can count the distance either up and down the y-axis or across the x-axis
Using Distance formula which says,
[tex]\sqrt{{({x}_2 - {x_1})}^2 + {({y}_2 - {y}_1)}^2} = r\\\sqrt{{(x - h)}^2 + {(y - k)}^2} = r\\\\{(x - h)}^2 + {(y - k)}^2 = r^2[/tex]
Hence, the equation of the new circle will be [tex]\\{(x - h)}^2 + {(y - k)}^2 = r^2[/tex]
Formula used:
[tex]\sqrt{{({x}_2 - {x_1})}^2 + {({y}_2 - {y}_1)}^2} = r[/tex]
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