Question

Question 4 Find the coordinates of a point on y-axis which are at a distance offrom the point P (3, –2, 5).

Class X1 - Maths -Introduction to Three Dimensional Geometry Page 279

Answer 1

Let any point on Y - axis is A ≡ ( 0, y , 0)
A/C to question,
distance between P and A = 5√2
Use distance formula ,
Distance between two points = √{(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)² }
⇒ 5 √2 = √{(3 - 0)² + (-2 - y )² + ( 5 - 0)² }
⇒ 5√2 = √{9 + (2 + y)² + 25 }
Take square both sides,
⇒ 25 × 2 = 34 + (2 + y )²
⇒ 50 - 34 = (2 + y)²
⇒ 16 = (2 + y)²
⇒4² = (2 + y)²
(2 + y) = ±4
y = -2 ±4
hence, y = -6 and 2

Hence, the point on Y -axis are ( 0, -6, 0) and ( 0, 2 ,0)