Circles intercepts questions

[JackSonSmith]

Find the radii and coordinates of the centre of the circles with equations
4x 2 + 4y 2 − 60x − 76y + 536 = 0 and x 2 + y 2 − 10x − 14y + 49 = 0, and find the
coordinates of the points of intersection of the two curves.

I have attached answer as image inside word document.

Could someone please explain how to get the answer of the intercepts of the two circles, I could work out the radius and centre.

[Tyleralp1]

EDIT: DISREGARD

Isn't finding the intercepts more or less the same for most graphs?

-To find the x-intercept, sub y=0 into the equation, transpose and solve for x.
-To find the y-intercept. sub x=0 into the equation, transpose and solve for y.

[brightsky]

Unfortunately, the process is a bit of a pain, but here's the working out:

Multiply both sides of the second equation by 4:
4x^2 + 4y^2 − 40x − 56y + 196 = 0

Subtract the first equation from the equation above:
(4x^2 + 4y^2 − 40x − 56y + 196) - (4x^2 + 4y^2 − 60x − 76y + 536) = 0
20x + 20y = 340
x + y = 17
y = 17 - x

Substitute the equation above into second equation provided in the question stem:
x^2 + y^2 − 10x − 14y + 49 = 0
x^2 + (17 - x)^2 - 10x - 14(17-x) + 49 = 0
2x^2 - 30x + 100 = 0
x^2 - 15x + 50 = 0
(x-10)(x-5) = 0
x = 10 or x = 5

Substituting these back into the equation y = 17 - x, we get the solutions: (x,y) = (10,7) and (5,12).

[Tyleralp1]

Oh, my apologies..

Please disregard my response. It appears I didn't read the question correctly *facepalm*

[keltingmeith]

Oh, my apologies..

Please disregard my response. It appears I didn't read the question correctly *facepalm*

Don't worry - I answered this question somewhere else a while ago, and did the exact same thing you did at first.