Question

the point (x,y) is a distane of exactly 4 units from the point (1,2) use the distnace formula to come up with an equation that x and y satisfies and simplify so it contins not square root sign.

Answer 1

To find an equation satisfying the distance condition, we can use the distance formula and substitute the given points. Squaring both sides of the equation and simplifying will give us the final equation.

Step-by-step explanation:

The distance formula is given by:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, we have the point (x,y) which is 4 units away from the point (1,2). We can substitute these values into the formula:

4 = sqrt((x - 1)^2 + (y - 2)^2)

Squaring both sides of the equation to eliminate the square root, we get:

16 = (x - 1)^2 + (y - 2)^2

Expanding and simplifying, we have:

16 = x^2 - 2x + 1 + y^2 - 4y + 4

Combining like terms, we get:

x^2 - 2x + y^2 - 4y - 11 = 0

So, the equation that satisfies the distance condition is x^2 - 2x + y^2 - 4y - 11 = 0.