Prove a circle has a tangent (1 Viewer)

[Redyapper]

Hi,

I need to prove that x^2+2x+y^2-4y-4=0 has the tangent 3x+4y+10=0.
How I've done previous questions like this is through simultaneous equations, then finding the discriminant, and if the discriminant=0, that means it's got one root and hence that's the tangent.

I just keep going wrong somewhere in this question, and I have no clue where so if someone could solve it so I could find what I'm doing wrong, it'd be great.

Thanks!

 

[nightweaver066]

Rearranging the tangent equation,

Subbing in to the equation for the circle,

 

[J-Wang]

When derivative is equal to 0, there is a tangent as shown by nightweaver

 

[Redyapper]

Rearranging the tangent equation,

Subbing in to the equation for the circle,

Thanks!

 

[Shadowless]

When derivative is equal to 0, there is a tangent as shown by nightweaver

*discriminant?

 

[Timothy6340]

wouldnt it be easier to find the radius of the circle and then do perpendicular distance formula from the the centre of the circle and the line and it the distances are = its a tangent

 

[nightweaver066]

wouldnt it be easier to find the radius of the circle and then do perpendicular distance formula from the the centre of the circle and the line and it the distances are = its a tangent

Yes.