Home
Class 12
MATHS
Find the least value of (x-1)^(2) + (y-2...

Find the least value of `(x-1)^(2) + (y-2)^(2)` under the condition 3x+4y -2 = 0.

Text Solution

Verified by Experts

`(x-1)^(2) + (y-2)^(2)` is square of distances between the points A(1,2) and P(x,y), where P lies on the line 3x +4y-2=0.
Least value of `(x-1)^(2) + (y-2)^(2)`
=Square of shortest distance of point (1,2) from the line 3x + 4y-2=0
`=((|3(1)+4(2)-2|)/(sqrt(3^(2) +4^(2))))^(2) = (9)/(25)`
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE|Exercise Exercise 2.1|23 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise Exercise 2.2|4 Videos

  • STRAIGHT LINE

    CENGAGE|Exercise Multiple Correct Answers Type|8 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise JEE Advanced Previous Year|9 Videos

Similar Questions

Explore conceptually related problems

Find the least value of (x-2)^(2)+(y-2)^(2) under the condition 3x+4y-2=0

Find x when the least value of 2x^(2)+3y^(2) under the conditions x+y=2,x>=0,y>=0 occurs.

The least value of 2x^(2)-4x+3y^(2)-18y+31 is

Find the value of x and y4x^(2)+4y-2=0,2x^(2)+6y=0

Find the least and greatest value of f(x,y) = x^(2) + y ^(2) - xy where x and y are connected by the relation x^(2)+4y^(2) = 4 .

Find the minimum value of (a^(2))/(x^(2))+(b^(2))/(y^(2))(a,b)in N under the condition a^(2)x^(2)+b^(2)y^(2)=1

Find the value of x and y- 2x+3y=0 3x+4y=5

Find the maximum value of x+y subjected to the condition 4x+3y le 12, 2x + 5y le 10, x le 0, x ge 0, y ge 0 .

Find the least and the greatest value of f(x , y) = x^(2) + y^(2) - xy where x and y are connected by the relation x^(2) + 4y^(2) = 4