Question

Use the distance formula to show algebraically and graphically that the following two circles do not intersect. (x-1)²+(y+2)²=1 ; (x+5)²+(y-4)²=4

Answer 1

Answer and Step-by-step explanation:

C1) (x-1)²+(y+2)²=1  C1 (1,-2) R1 = √1 = 1

C2) (x+5)²+(y-4)²=4 C2 (-5,4) R2 = √4 = 2

DISTANCE FORMULA: d² = (y₂-y₁)²+(x₁-x₂)²

calculating the distances between the 2 center:

d² = (4-(-2))²+(-5-1)² = (6)²+(-6)² = 36 + 36 = 72 ⇒ d = √72

√72 ≈ 8.49

R1 = 1 and R2 = 2

If the circles were secants, d would be < than R1 + R2.

If the circles were tangent, d would be = to  R1 + R2

As d > than R1 + R2, we know that the circles do not intercept.