For two circles x2 + y2 = 16 and x2 + y2 - 2y = 0, there is / are1. O

1.	For two circles x2 + y2 = 16 and x2 + y2 - 2y = 0, there is / are1. One pair of common tangent2. Two pair of common tangents3. Three pair of common tangents4. No common tangents
Answer» Correct Answer - Option 4 : No common tangents CONCEPT : The distance between the centres of two circle is less than the difference of their radii then there is no common tangent. CALCULATION: Equation of first circle x2 + y2 = 16 which can be re-written as: x2 + y2 = 4² So, the centre of the first circle (0,0) and radius = 4 Equation of second circle x2 + y2 - 2y = 0 which can be re-written as: x2 + (y-1)² = 1² So, the centre of the second circle is: (0,1) and radius = 1 So, the distance between the centres \(d = \sqrt {{0^2} + {1^2}} = 1\) The difference between the radii of the two circles = \|4 - 1\| = 3 As we can see that, the distance between the centres < difference of their radii We also know that if the distance between the centres of two circle is less than the difference of their radii then there is no common tangent. So there is no common tangent between the two given circles. Hence, option D is the correct answer.

For two circles x2 + y2 = 16 and x2 + y2 - 2y = 0, there is / are1. One pair of common tangent2. Two pair of common tangents3. Three pair of common tangents4. No common tangents

Answer» Correct Answer - Option 4 : No common tangents

CONCEPT :

The distance between the centres of two circle is less than the difference of their radii then there is no common tangent.

CALCULATION:

Equation of first circle x2 + y2 = 16 which can be re-written as: x2 + y2 = 4²

So, the centre of the first circle (0,0) and radius = 4

Equation of second circle x2 + y2 - 2y = 0 which can be re-written as: x2 + (y-1)² = 1²

So, the centre of the second circle is: (0,1) and radius = 1

So, the distance between the centres \(d = \sqrt {{0^2} + {1^2}} = 1\)

The difference between the radii of the two circles = |4 - 1| = 3

As we can see that, the distance between the centres < difference of their radii

We also know that if the distance between the centres of two circle is less than the difference of their radii then there is no common tangent.