Question

The equation of the set of points whose distance from the point (2,-1, 3) is 5 units is

Answer 1

we have to find the equation of the set of points whose distance from the point (2, -1, 3) is 5 units.

solution : let locus of the point lying on the equation of the sets of points whose distance from the point (2, -1, 3) is 5 units is (x , y, z).

using distance formula,

distance between (x, y, z) and (2, -1, 3) is given by, √{(x - 2)² + (y + 1)² +(z - 3)²}

so, 5 = √{(x - 2)² + (y + 1)² +(z - 3)²}

squaring both sides we get,

⇒5² = (x - 2)² + (y + 1)² +(z - 3)²

⇒(x - 2)² + (y + 1)² +(z - 3)² - 25 = 0

Therefore the equation of the sets of points whose distance from the point (2, -1, 3) is 5 units is (x - 2)² + (y + 1)² +(z - 3)² - 25 = 0.