If the line b x+m y+n=0 is tangent to the parabola y²=4 a x , then

Step-by-step solution

Given, parabola, y²=4 a x array lr & 2y d y d x =4 a d y d x = 2 a y array which is the slope of tangent. Given, l x+m y+n=0 is an equation of tangent of the parabola y²=4 a x Slope of tangent =- l m From Eqs. (i) and (ii) aligned 2 a y &=- l m y= -2 a m l & y²=4 a x 4 a² m² l² &=4 a x & x= a m² l² aligned On putting the values of x and y in the following equation aligned b x+m y+n &=0 l ( a m² l² )+m ( -2 a m l )+n &=0 a m² l - 2 a m² l +n &=0 a m² l =n a m² &=n l aligned which is the required relation.