If a number of ellipses whose major axis is x -axis and the minor axis is y -axis be described having the same length of the major axis as 2 but a variable minor axis, then the tangents at the ends of their latus rectum pass through fixed points whose distance from the centre is equal to

Step-by-step solution

Since the minor axis is variable, hence e is a variable quantity Therefore the equation of the tangent to the ellipse can be written as x a e a 2 + y b 2 a b 2 = 1 ⇒ e x + y = a ⇒ y - a + e x = 0 This line passes through the fixed point 0 , a (where a = 1 ) Hence, distance fro the centre of the ellipse = 1