Final answer:
The area of triangle OAB is 0.5 * ab. Option A is correct.
Step-by-step explanation:
In order to find the area of triangle OAB, we first need to find the coordinates of points A and B. Let's assume the equation of the ellipse is x^2/a^2 + y^2/b^2 = 1 and the slope of the tangent line is m. As the line intersects the major and minor axes at A and B respectively, the coordinates of A are (a, ma) and the coordinates of B are (mb, b).
The area of triangle OAB can be found using the formula: Area = (1/2) * base * height. The base is the distance OA, which is a in length, and the height is the distance from B to the x-axis, which is b. Substituting the values, we get:
Area = (1/2) * a * b = 0.5 * ab
The question is asking to find the area of the triangle formed by the points where a tangent to an ellipse intersects the major and minor axis, and the origin. The tangent intersects the major axis (length 2a) at point A and the minor axis (length 2b) at point B. The area of a triangle can be calculated by taking half the product of its base and height.
Here, the base is the segment on the major axis (2a) and the height is the segment on the minor axis (2b). Thus, the area of triangle OAB would be (1/2)*(2a)*(2b) = ab