The equations of the tangents to the ellipse x^2 16 + y^2 9 = 1 making an inclination of 30^ with the major axis are

Step-by-step solution

The equation of the ellipse is x^2 16 + y^2 9 = 1 . Here, a^2 = 16 and b^2 = 9 . The tangent makes an angle of 30^ with the major axis (x-axis), so the slope of the tangent is m = 30^ = 1 3 . The equation of the tangent to the ellipse x^2 a^2 + y^2 b^2 = 1 with slope m is given by y = mx a^2 m^2 + b^2 . Substituting the values of a^2 , b^2 , and m , we get: y = 1 3 x 16 ( 1 3 )^2 + 9 y = 1 3 x 16 3 + 9 y = 1 3 x 16 + 27 3 y = 1 3 x 43 3 Multiplying the entire equation by 3 , we obtain: 3 y = x 43 x - 3 y 43 = 0 Ans