Let the line y = m x and the ellipse 2 x 2 + y 2 = 1 intersect at a point P in the first quadrant. If the normal to this ellipse at P meets the co-ordinate axes at - 1 3 2 , 0 and 0 , β , then β is equal to

Question

Let the line y = m x and the ellipse 2 x 2 + y 2 = 1 intersect at a point P in the first quadrant. If the normal to this ellipse at P meets the co-ordinate axes at - 1 3 2 , 0 and 0 , β , then β is equal to, 2 2 3, 2 3, 2 3, 2 3

MARKS App · Accepted Answer

Let P be x 1 , y 1 Equation of normal at P is x 2 x 1 - y y 1 = - 1 2 It passes through - 1 3 2 , 0 ⇒ - 1 6 2 x 1 = - 1 2 ⇒ x 1 = 1 3 2 So, y 1 = 2 2 3 (as P lies in Ist quadrant) So, β = y 1 2 = 2 3

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