Question

Find the distance between the centers of the two circles with equations below, and use that distance to determine in how many points these circles intersect. x²+y²=5 ; (x-2)²+(y-1)²=3

Answer 1

Answer: two circles are intersecting each other at two points

Explanation:

c1 - x²+y²=5 c1 (0,0) R1 = √5

c2 - (x-2)²+(y-1)²=3 c2 (2,1) R2 = √3

D² = (x2−x1)²+(y2−y1)²

D² = (1-0)²+(2-0)² = 1 + 4 = 5 ⇒ D = √5

As √5 + √3 > D > √5 - √3 we know that the two circles are intersecting each other at two points