Question

Find the area of the smallest triangle formed by the x axis, y axis, and a line that goes through the point (4,2). Type an integer or a number with two decimal points. Area :

Answer 1

- let, for the line passing through the point (4,2), the geintercept ab and the n-intercepta. Then, the area of the triangle is in A = a.b. I we know that (0,6) and (4,2) lie on the line. So, slope of the line- m= 2-b y = ? So, the equation of the line is - y = 2.b xtb. since, it cuts a anis at (90), so de zob. a to ДЬ b -2 - 1 Area, 46.b H = 6-2 262 & A. (b) = b for Now we find the critical value of b which I is minimum A 16-2346 - 235 2 (6-2) 2 46²-86-262 16-2²

- 26-86 a ab (6-4) (6-22 foro, da so gives b20 or b=4. of b=0, then it does not form a truangle. So b=4. is a critical point.. Now, da _ (6-2) ? (Ab-8)= (25-86) (6-2). Sone 32 = 270 for b=4. . I is minimum at b=4 (by second derivative test). . Sob=4, a = 4x4 - 8 - 2 - Area of the triangle is. Antxaxbat x 4x8 X = 16 Drea of the required smallest teangle is 16.