My Flower Basket delivers flowers within a 25 mile radius of their store. If this area is represented graphically, with My Flower Basket located at (4, 3), what is the equation that represents the delivery area?
To determine the equation that represents the delivery area, we need to use the distance formula. The distance formula is √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) represents the coordinates of My Flower Basket (4, 3), and (x2, y2) represents the coordinates of any point within the delivery area.
Since the delivery area extends within a 25-mile radius, any point (x, y) within this area will have a distance that is less than or equal to 25 miles from the coordinates of My Flower Basket.
Using the distance formula, we can set up the equation:
√((x - 4)^2 + (y - 3)^2) ≤ 25
This equation represents the delivery area for My Flower Basket within a 25-mile radius.
To find the equation that represents the delivery area, we can use the distance formula to calculate the distance between My Flower Basket and any point (x, y) within the delivery area.
The distance formula is given by:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Where (x1, y1) represents the coordinates of My Flower Basket, and (x2, y2) represents the coordinates of any point within the delivery area.
In this case, the coordinates of My Flower Basket are (4, 3). Let's substitute these values into the distance formula.
Distance = sqrt((x - 4)^2 + (y - 3)^2)
Since the delivery area is defined as within a 25 mile radius, we can set the distance equal to 25 and solve for y.
25 = sqrt((x - 4)^2 + (y - 3)^2)
Now, to find the equation, we square both sides of the equation to eliminate the square root.
625 = (x - 4)^2 + (y - 3)^2
Expanding the equation and simplifying, we get:
625 = x^2 - 8x + 16 + y^2 - 6y + 9
Rearranging the terms, we have:
x^2 + y^2 - 8x - 6y = 600
Therefore, the equation that represents the delivery area of My Flower Basket is:
x^2 + y^2 - 8x - 6y = 600