Question

Find the relation between x and y when the point Q(x,y) has the property that dist(Q,P₁)+dist(Q,P₂)=4 with respect to points P₁ (0,−1),P₂(0,1). Y²− (X²/3) = 1

Answer 1

To find the relation between x and y, we can calculate the distance between point Q and points P₁ and P₂ using the distance formula. Then, by simplifying and solving for y, we can express the relation as y = ±√(4 - (x²/3)).

Step-by-step explanation:

The given question is asking us to find the relation between x and y when the point Q(x,y) has the property that dist(Q,P₁)+dist(Q,P₂)=4 with respect to points P₁ (0,−1),P₂(0,1).

To find the relation between x and y, we can start by calculating the distance between Q and P₁ and the distance between Q and P₂. The distance formula is given by the equation: √((x₂ - x₁)² + (y₂ - y₁)²).

Applying the distance formula, we have: √((x - 0)² + (y - (-1))²) + √((x - 0)² + (y - 1)²) = 4.

Simplifying and solving for y, we get: y = ±√(4 - (x²/3)).