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For the ellipse given by x²/9 + y²/4 = 1, let S(p, q) represent a point in the first quadrant such that p²/9 + q²/4 > 1. From S, two tangents are drawn to the ellipse: one touches the ellipse at an endpoint of the minor axis, while the other intersects the ellipse at a point T located in the fourth quadrant. Let R be the vertex of the ellipse with the positive x-coordinate, and O be the center of the ellipse. If the area of triangle ΔORT is 3/2, which of the following is true?

1. q = 2 and p = 3√3
2. q = 2 and p = 4√3
3. q = 1 and p = 5√3
4. q = 1 and p = 6√3

Correct answer: q = 2 and p = 3√3

Solution

The correct option is true because the area of triangle ΔORT is given as 3/2, and using the equation of the ellipse and the properties of tangents, we can derive the values of p and q that satisfy this condition, which are q = 2 and p = 3√3.

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