Question

Write the equation of a circle with a center (10,7) and a radius of 2

Answer 1

(x - 10)^2 + (y - 7)^2 = 2^2

Explanation:

Start with the standard equation of a circle with center (h, k) and radius r:

(x - h)^2 + (y - k)^2 = r^2

Substitute 10 for h, 7 for k and 2 for r, obtaining:

(x - 10)^2 + (y - 7)^2 = 2^2

Answer 2

x ^2 + y^2 - 20x + 14y + 145 = 0

Explanation:

The formula for equation of a circle is (x- h) ^2 + (y + k) ^2 = r^2

(h,k) is the center

r is the radius

Inserting the values (10,7)

h -10

k - 7

Inserting into the above formula

( x - 10)^2 + ( y + 7)^2 = 2^2

(x - 10)(x - 10) + (y + 7)(y + 7) = 4

Opening the brackets

= (x ^2 - 20x + 100) + (y^2 + 14y + 49) = 4

x^2 - 20x + 100 + y^2 + 14y + 49 = 4

Rearranging algebrally,

x^2 + y^2 - 20x + 14y + 100 + 49 - 4 = 0

= x^2 + y^2 - 20x + 14y + 145 = 0