Final answer:
The question involves finding the equation of an ellipse with foci at A(4,0,0) and B(-4,0,0) for which the sum of the distances from any point on the ellipse to the foci is constant (10). The equation of an ellipse is based on the sum of distances to the two foci being constant, not on solving a quadratic equation.
Step-by-step explanation:
The question asks to find the equation of an ellipse where the sum of the distances from any point P on the ellipse to two fixed points A(4,0,0) and B(-4,0,0) is equal to 10.
This is a classic definition of an ellipse, where A and B are the foci of the ellipse and the sum of distances PF1 (from P to focus A) and PF2 (from P to focus B) is constant (10 in this case).
This equation can be described as:
PF1 + PF2 = 10
We do not need to use the quadratic equation here, as that pertains to solving quadratic equations of the form at² + bt + c = 0, which is not required for describing the equation of an ellipse.