Select the correct answer.A circle is described by the equation x2 + y2 + 14x + 2y + 14 = 0. What are the coordinates for the center of the circle and the length of theA.(-7, -1). 36 units'B.c.D.(7.1). 36 units(7.1), 6 units(-7, -1), 6 unitsNext
Accepted Solution
A:
Answer:(- 7, - 1), 6 unitsStep-by-step explanation:The equation of a circle in standard form is(x - h)² + (y - h)² = r²where (h, k) are the coordinates of the centre and r is the radius.Givenx² + y² + 14x + 2y + 14 = 0Collect x/y terms together and subtract 14 from both sidesx² + 14x + y² + 2y = - 14To obtain standard form use the method of completing the squareadd ( half the coefficient of the x/y terms )² to both sidesx² + 2(7)x + 49 + y² + 2(1)y + 1 = - 14 + 49 + 1(x + 7)² + (y + 1)² = 36 ← in standard formwith centre (- 7, - 1) and radius = [tex]\sqrt{36}[/tex] = 6