If the sum of squares of distances of the point (x,y) from the points (a,0) and (-a,0) is `2b^2`, then:

Options

A. `x^2+a^2=b^2-y^2`
B. `x^2+a^2=2b^2-y^2`
C. `x^2-a^2=b^2+y^2`
D. `x^2+a^2=b^2y^2`

Answer

To solve the problem step by step, we need to find the relationship between the point \((x, y)\) and the points \((a, 0)\) and \((-a, 0)\) based on the given condition regarding the sum of squares of distances.

### Step 1: Write the distance formula
The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]