common tangent to the given equations

Question

kanwal32 · Answer

attachment

kanwal32 · Answer

@Directrix

directrix · Answer

Did you graph the two circles?

directrix · Answer

Here are the two graphs. They appear to touch in a single point.

directrix · Answer

How many common tangent?  @kanwal32

kanwal32 · Answer

1

kanwal32 · Answer

@Directrix how will i do this in exam 
in a faster way

samigupta8 · Answer

Just make a graph and that will be the easiest way to analyse this situation..

samigupta8 · Answer

A rough sketch would also make it clear though and not necessarily the better layout (exact graphical ) i mean..

directrix · Answer

>1

One common external tangent is correct

directrix · Answer

I don't know of a fast way to do this.

You could solve the equations simultaneously:

x^2 + y^2 = 4  
 x2 + y2 -6x -8y = 24

to get at most 2 points of intersection.

We do know that this system intersects in one real point.

That means one tangent.

samigupta8 · Answer

@jiteshmeghwal9 u didn't take into consideration the diff of the two circles radii..
Analyse it and u will get one common tangent