Tangents are drawn from the external point P(2, 3) to the ellipse x^2 + 4y^2 = 20 . The square of the length of their chord of contact is

Step-by-step solution

The equation of the chord of contact from an external point (x₁, y₁) to the ellipse is given by T = 0 . For the point P(2, 3) and the ellipse x^2 + 4y^2 = 20 , the chord of contact is: x(2) + 4y(3) = 20 2x + 12y = 20 x + 6y = 10 x = 10 - 6y To find the points of contact, substitute x = 10 - 6y into the ellipse equation: (10 - 6y)^2 + 4y^2 = 20 100 - 120y + 36y^2 + 4y^2 = 20 40y^2 - 120y + 80 = 0 y^2 - 3y + 2 = 0 Solving this quadratic equation: (y - 1)(y - 2) = 0 y = 1 or y = 2 Now, find the corresponding x-coordin