JEE Advanced 2018 Mathematics question

Consider two straight lines, each of which is tangent to both the circle and the parabola . Let these lines intersect at the point . Consider the ellipse whose center is at the origin and whose semi-major axis is . If the length of the minor axis of this ellipse is , then which of the following statement(s) is (are) TRUE?

• (A)For the ellipse, the eccentricity is and the length of the latus rectum is 1Correct
• (B)For the ellipse, the eccentricity is and the length of the latus rectum is
• (C)The area of the region bounded by the ellipse between the lines and is Correct
• (D)The area of the region bounded by the ellipse between the lines and is