Question

p(5,5) is a point inside the circle x^2+y^2-4x-6y-12=0. if the origin is translated to a certain point and transformed equation is x^2+y^2=25​

Answer 1

Therefore the origin is translated to P(2,3).

Step-by-step explanation:

If the origin translated to P(a,b)

Then x=x'+a   and y=y'+b

     x'= x-a             y'=y-b

Therefore the equation (x²+y²) =25 becomes

(x-a)²+(y-b)²=25

⇒x²-2ax+a²+y²-2by +b²=25..........(1)

Given equation is

x²+y²-4x-6y-12=0..............(2)

Comparing the coefficient of x and y

-2ax = -4x

 ⇒a = 2                      

and  -2by= -6y

⇒ b=3

Therefore the origin is translated to P(2,3).