Question

Determine the centre and radius of the circle with equation 

x² +10x + y² - 14y = -70.

Answer 1

x² +10x + y² -14y +70= 0 x² + 10x + 25 - 25 y² + y² – 14y + 49-49 +70= 0 (x+5)² + (y-7)²+74-70=0 (x-(-5))² + (y-7)² = 2² Compare it with eqn (x-h)² + (y-k)² = r² So therefore h = -5 y= 7 r = 2

Answer 2

SOLUTION :

Equation of circle :

x^2 + 10x + y^2 - 14 y = - 70

=> (x + 5)^2 - 5^2  + (y - 7)^2 - 7^2 = - 70

=> (x + 5)^2 + (y - 7)^2 = - 70 + 5^2 + 7^2 = 4

=> (x + 5)^2 + (y - 7)^2 = 2^2 

This is of the form :

(x + h)^2 + (y - k)^2 = r^2 having centre at (- h, k) and radius r.

So,

Centre of the given circle is (- 5, 7) and radius is 2 (ANSWER).