Question

Find point on 2x+3y=6 which is closest to the origin

Answer 1

Answer:

Step-by-step explanation:

(0, 0) (x,y) where y = 2x + -3  

(0,0) (x, 2x+ -3)  

Now you have to use the distance formula:  

D= √(x² +y²)  

D= √(x² + (2x+ -3)²)  

D=√ (x² + 4x² + -12x +9)  

D=√(5x² + -12x + 9)  

Now you have to take the derivative and set it to 0.  

D'= 10x+ -12 / 2√(5x² + -12x + 9) = 0  

D' = 5x + -6 / √(5x² + -12x + 9) = 0  

Since we only need to numerator to = 0 for the whole thing to be 0 we do the following:                                                                                                         5x + -6= 0  

Solve for x  

5x = 6  

x = 5/6  

Now we need to find y:  

y=2x+ -3  

y=2(5/6) + -3  

y= -4/3

Answer: (5/6 , -4/3)  

Hope that was helpful!