Find the values of x; y for which x^2 + y^2 takes the minimum value where (x + 5)^2 + (y-12)^2 = 14^

ankit jhunjhunwala

Find the values of x; y for which x^2 + y^2 takes the minimum valuewhere (x + 5)^2 + (y-12)^2 = 14^2.

Sujit

the x,y lie on the below circle with centre A(-5,12)

x²+y² implies distance of any point on the circle from the origin

for distance to be minimum the point should lie on the normal of the circle which passes through origin

as radius is 14 and distance between centre and origin is 13

thus minimum value of x²+y²=1

Deepak Aggarwal

Using triangular inequality,

So, minimum ( x² + y² ) = 1

Solving the equaitons now, you'll get

x = 5 / 13 and y = - 12 / 13