Question

Find an equation set of all points equidistant from the points S=(-1,2,-5).

What is the equation representing the set of points equidistant from point S(-1, 2, -5)?
a) x + y + z = 0
b) x - y + z = 0
c) x + y - z = 0
d) x - y - z = 0

Answer 1

To find an equation representing the set of points equidistant from point S (-1, 2, -5), use the distance formula and simplify the resulting expression. Set the equation equal to a constant value and simplify further to get the equation x + y + z + 2 = C. Therefore, the correct option is a) x + y + z = 0.

Step-by-step explanation:

To find an equation representing the set of points equidistant from point S (-1, 2, -5), we need to find the locus of points that are equidistant from S. The distance between a point (x, y, z) and S is given by the formula:

d = √((x - (-1))^2 + (y - 2)^2 + (z - (-5))^2)

To simplify the equation, we can expand and simplify the expression:

d = √(x^2 + y^2 + z^2 + 2x + 4y + 10z + 30)

Now we can set the equation equal to a constant value to represent all the points that are equidistant from S:

x^2 + y^2 + z^2 + 2x + 4y + 10z + 30 = C

Where C is the constant value. Simplifying the equation further, we get:

x + y + z + 2 = C

So, the equation representing the set of points equidistant from point S is x + y + z + 2 = C. Therefore, the correct option is a) x + y + z = 0.