NIMCET 2019 Mathematics PYQ — For two circles and , there is / are… | Mathem Solvex | Mathem Solvex
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NIMCET 2019 — Mathematics PYQ
NIMCET | Mathematics | 2019
For two circles x2+y2=16 and x2+y2−2y=0, there is / are
Choose the correct answer:
A.
One pair of common tangent
B.
Two pair of common tangents
C.
Three pair of common tangents
D.
No common tangents
(Correct Answer)
Correct Answer:
No common tangents
Explanation
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=02+12=1
The difference between the radii of the two circles =|4-1|=3
As we can see that, the distance bettveen the centres < difference of their radii We also know that if the distance betveen the centres of two circle is less than the difference of their radii then So there is no common tangent between the two given circles. Hence, option D is the correct answer.
Explanation
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=02+12=1
The difference between the radii of the two circles =|4-1|=3
As we can see that, the distance bettveen the centres < difference of their radii We also know that if the distance betveen the centres of two circle is less than the difference of their radii then So there is no common tangent between the two given circles. Hence, option D is the correct answer.
