Question

the power of (-1,1) with respect to the circle x^2+y^2-6x+4y-12=0 is please Urgently required​

Answer 1

Given:

point = (-1, 1)

$\bold{\ Equation =\ x^2+y^2-6x+4y-12 =0}$

To find:

radius =?

Solution:

In the given question point and an equation is given at this we find the center of the circle that is: (3, -2)

Points:  (-1, 1) and (3, -2)

$x_1 =-1\\y_1= 1\\x_2= 3\\y_2= -2$

Distance formula:

$D= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$D= \sqrt{(3+1)^2+(-2-1)^2}\\\\D= \sqrt{(4)^2+(-3)^2}\\\\D= \sqrt{16+9}\\\\D= \sqrt{25}\\\\D= 5$

The radius  value is = 5.