x^+ y^ + 4x -2y - 20 = 0 find the center, radius and all interceps of the cricle.?

Question

Please be detailed..

Answer 1

(x - h)^2 + (y - k)^2 = r^2 is the equation for the circle. In this case, first you have to get it into this form.

Start by grouping terms:

x^2 + y^ + 4x - 2y - 20 = 0 -----> (x^2 + 4x) + (y^2 - 2y) = 20

Next complete the square for each binomial, but make sure you add number to BOTH sides of the equation:

(x^2 + 4x) + (y^2 - 2y) = 20 ---->
(x^2 + 4x + 4) + (y^2 - 2y + 1) = 20 + 4 + 1
(x + 2)^2 + (y - 1)^2 = 25
(x + 2)^2 + (y - 1)^2 = 5^2

So, (h,k) = (-2, 1) is the center
r = 5 is the radius

x-intercepts are found by setting y = 0
(x + 2)^2 + (0 - 1)^2 = 5^2
x^2 + 4x + 4 + 1 = 25
x^2 + 4x - 20 = 0
x = [ -4 +/- sqrt( (4^2) - (4)(1)(-20) ) ] / 2
= [ -4 +/- sqrt(96) ] / 2
[ - 2 +/- 2sqrt(6) ]

y-intercepts are found by setting x = 0
(0 + 2)^2 + (y - 1)^2 = 5^2
y^2 - 2y + 1 + 4 = 25
y^2 - 2y - 20 = 0
y = [ 2 +/- sqrt( (-2^2) - (4)(1)(-20) ) ] /2
= [ 1 +/- sqrt(21) ]

Answer 2

x^2 + y^2 - 4x - 2y - 20 = 0
x^2 - 4x + y^2 - 2y - 20 = 0
(x^2 - 4x) + (y^2 - 2y) - 20 = 0
(x^2 - 4x + 4 - 4) + (y^2 - 2y + 1 - 1) - 20 = 0
((x - 2)^2 - 4) + ((y - 1)^2 - 1) - 20 = 0
(x - 2)^2 - 4 + (y - 1)^2 - 1 - 20 = 0
(x - 2)^2 + (y - 1)^2 - 25 = 0
(x - 2)^2 + (y - 1)^2 = 25

since the standard form for a circle is

(x - h)^2 + (y - k)^2 = r^2
(h,k) being the center and r being the radius

Center : (2,1)
Radius : 5

(x - 2)^2 + (y - 1)^2 = 25

(0 - 2)^2 + (y - 1)^2 = 25
(-2)^2 + (y - 1)^2 = 25
4 + (y - 1)^2 = 25
(y - 1)^2 = 21
y - 1 = sqrt(21)
y = 1 ± sqrt(21)

(x - 2)^2 + (0 - 1)^2 = 25
(x - 2)^2 + (-1)^2 = 25
(x - 2)^2 + 1 = 25
(x - 2)^2 = 24
x - 2 = sqrt(24)
x - 2 = sqrt(4 * 6)
x - 2 = 2sqrt(6)
x = 2 ± 2sqrt(6)

ANS :

Center : (2,1)
Radius : 5
Intercepts : (((2 + 2sqrt(6)),0), (((2 - 2sqrt(6)),0), (0,(1 + sqrt(21))), (0,(1 - sqrt(21)))

Answer 3

x^2 + y^2+4x -2y - 20 =0
(x^2+4x)+(y^2-2y) = 20
(x+2)^2 -4 +(y-1)^2 -1 = 20
(x+2)^2 +(y-1)^2 = 25 = 5^2
so centre is x = -2 y = -1
radius = 5
intercepts can be calucated by putting x = 0 and finding y
as similarly

Answer 4

DO I HAVE TO..I USUALLY PAY A NERD TO DO MY HOMEWORK FOR ME!

CAN I USE THE CIRCLE PLATE TO MAKE MY APPLE PIE?? ENJOY LOOKING FOR THE RADIUS WHILE EATING THE PIE!

WHILE YOU ARE AT IT FIND THE RADIUS OF A PIZZA OKAY...HOPEFULLY YOU WILL HAVE PIZZA LEFT AFTER CALCULATING THE CENTER!