Question

Determine the center and radius and make the circle graph

x^2 - 8x + y^2 - 10y = -5

Answer 1

Given   - 8x + -10y = -5

Let us make the equation in terms of square by completing square method.

Consider - 8x = -2(4)x [ Here a = x and b = 4 ]

= - 2(4)x + (4*4) - (4*4)

= - 16

Consider - 10y =   -2(5)y [ Here a = y and b = 5]

= -2(5)y + (5*5) - (5*5)

= - 25

Thus, -8x + -10y = - 16 + - 25

= + - 41

But given -8x + -10y = -5

Thus, + -41 = -5

Then +   = -5 + 41

Hence, the equation is + = 36

Comparing it with the equation of circle

(x -a)2 + (y-b)2 = r2 where (a,b) is the centre and radius is r2

So, (a, b) = (4,5) and r2 = 36 implies r = 6

Thus, the centre is ( 4 , 5 )  and radius is 6

Now, keeping centre in (4,5) with radius 6 , a circle is constructed.