IIT JEE , AIEEE Forum - Mathematics , Analytical Geometry

deep01

Find the number of common tangents to the circles x²+y²=4 and x²+y²-6x-8y=24??

pls. explain ur answer

aditya_arora04

Hi,

Look,

When you draw the diagrams, you will see that the circles do not intersect or touch each other.

Hence, there are 4 different common tangents to the circles.

Do tell me if i am wrong. And, you can make a rough diagram easily.

You don't have to do any calculations and a lot of time is saved !!!!

khyatigupta

no aditya u gt the wrong ans as the two circles will touch each other internally at a pt.

since centres of the two circles are C1(0,0) having radius 2 and C2(3,4) having radius 7. hence C1C2=5 which is less than sum of its radii(7+2=9).

and also C1C2= difference of the radii.

thus the circles will touch each other internally.

there is only 1 common tangent.

i think thts the solution....

thanx

pink_ele

the simplest method is to solve two equations

if they intersect at 2 points then no of tangents is 2

if they touch then if first one lies inside no of tangents= 1

'""""""""""""""out side """""""""""""=3

if they dont touch then nof tagent is 4 or zero (if one lies inside other)

iitkgp_bipin

Centre of the two circles : C₁ = (0,0) ; C₂ = (3,4)

Radius of the two circles : r₁ = 2 ; r₂ = 7

Distance between thr centres = C₁C₂ = 5 which is the difference between the radius of the two circles.

Hence 1st circle touches 2nd circle internally.

Hence 1 common tangent is possible.

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