Question

The equations of the pair of straight lines parallel to the x-axis and tangent to the ellipse x²/4 + y²/9 = 1 are

 (A)  y = -3,y = 6

(B)  y = 3, y = -6

(C)  y = ± 6

(D)  y = ±3

Answer 1

Correct option  (D)  y = ±3

Explanation :

 Let y = k be a line parallel to x-axis. The points of intersections of the line with the ellipse are given by the equation 9x² + 4k² = 36

 which touches the ellipse. Solving we get

4k² = 36  or k = ±3.