Minimizes the sum of the two distance, Mathematics

The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as a/b where a and b are coprime positive integers. Find a+b.

Solution) The minimum distance of the points from (1,y) is the distance from the intersection of their perpendicular bisectors to the line x=1
hence slope of perpendicular bisector=> -4=2y-14 / 2x -7
                                                           => 8x + 2y = 42.

                                                         putting x=1,y=17,
                                                         hence a+b= 17 +1 =18 (ANS).

Posted Date: 3/29/2013 5:19:51 AM | Location : United States







Related Discussions:- Minimizes the sum of the two distance, Assignment Help, Ask Question on Minimizes the sum of the two distance, Get Answer, Expert's Help, Minimizes the sum of the two distance Discussions

Write discussion on Minimizes the sum of the two distance
Your posts are moderated
Related Questions
(3x+2)^2 d^2y/dx^2+3(3x+2)dy/dx-36y=3x^2+4x+1

Find out the volume of the solid obtained by rotating the region bounded by y = x 2 - 2x and  y = x about the line y = 4 . Solution: Firstly let's get the bounding region & t

Consider the following system of linear equations. X 1 +x 3 +x 4 = 2 X 1 +x 2 +x 3 = 6 X 2 +x 3 +x 4 = 3 X 1 +x 2 +x 4 = 0  (a) Write out the augmented matrix fo

Explain how we Converting Fractions to Percents ? To convert a fraction to a percent: 1. Convert the fraction to a decimal using long division. 2. Move the decimal point two p

Determine dy & Δy  if y = cos ( x 2 + 1) - x as x changes from x = 2 to x = 2.03 .  Solution Firstly let's deetrmine actual the change in y, Δy . Δy = cos (( 2.03) 2

1) Find the are length of r(t) = ( 1/2t^2, 1/3t^3, 1/3t^3) where t is between 1 and 3 (greater than or equal less than or equal) 2) Sketch the level curves of f(x,y) = x^2-2y^2

Q. How to add fractions Involving Negative Numbers? Ans. Adding fractions involving negative numbers, and subtracting them, are only slightly different. But, I'll write do

The product of -7ab and +3ab is (-7 x 3) a 2  b 2  = -21a 2  b 2 . In other words, a term with minus sign when multiplied with a term having a positive sign, gives a product having

If 7 cosec?-3cot? = 7, prove that 7cot? - 3cosec? = 3. Ans:    7 Cosec?-2Cot?=7 P.T 7Cot? - 3 Cosec?=3 7 Cosec?-3Cot?=7 ⇒7Cosec?-7=3Cot? ⇒7(Cosec?-1)=3Cot? ⇒7(C