A line is drawn through the point (1,2) to meet the co-ordinate axes at P and Q such that it forms a O P Q , where O is the origin. If the area of O P Q is least, then the slope of the line PQ is

Step-by-step solution

The equation of line PQ passing through (1,2) is y-2= m (x-1) aligned A ( OPQ )= 1 2 OP OQ & & = 1 2 (1- 2 ~m )(2- m ) & = 1 2 (4- m - 4 ~m ) A & =2- m 2 - 2 ~m dA dm & =- 1 2 + 2 ~m ^2 Now & dA dm =0 - & 1 2 + 2 ~m ^2 =0 m ^2 & =4 m & = 2 d ^2 ~A dm ^2 & =- 4 ~m ^3 At m & =2 d ^2 ~A dm ^2 & 0 aligned Area of OPQ will be least at m =-2 Slope of the line P Q=-2