Question

From a point p two tangents are drwan to the elllipse x²/a² + y²/b² = 1 if theses tangents intersect the coordinate axes at concyclic points , then the locus of the point p is (a>b)

a. x²+y² = a²+b²
b. x²+y² = a²-b²
c. x²-y² = a²-b²
d. x²=y²

Answer 1

The locus of the point P from which two tangents are drawn to the ellipse x²/a² + y²/b² = 1, intersecting the coordinate axes at concyclic points, is given by x² + y² = a² + b².

Step-by-step explanation:

The locus of the point P from which two tangents are drawn to the ellipse x²/a² + y²/b² = 1, intersecting the coordinate axes at concyclic points, is given by x² + y² = a² + b² (option a).

To understand this, we need to consider the properties of an ellipse. An ellipse is a closed curve such that the sum of the distances from any point on the curve to the two foci is constant.

In this case, the two tangents are drawn from point P to the ellipse. As these tangents intersect the coordinate axes at concyclic points, it means the distances from point P to the foci of the ellipse are equal. Therefore, the sum of the distances from point P to the foci is constant and equal to a² + b².