If `x , y in R` satisfies `(x+5)^2+(y-12)^2=(14)^2,` then the minimum value of `sqrt(x^2=y^2)` is__________

Answer

1

Explanation

Let `x = 5 = 14 cos theta and y -12 = 14 sin theta`
`therefore x ^(2) +y^(2) = (14 cos theta - 5)^(2) + (14 sin theta + 12)^(2)`
`" " = 196 + 25 + 144 + 28 ( 12 sin theta - 5 cos theta)`
` " "= 365 + 28(12 sin theta - 5 cos theta)`
` therefore sqrt(x^(2) + y^(2)) :|_(min)= sqrt(365- 28 xx 13)`
`" " =sqrt(365 - 364) = 1`