Review question

# Can we find the tangents to a circle from a point? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6804

## Suggestion

Prove that the line $y=mx+c$ will touch the circle $x^2+y^2=25$ if $c^2=25(1+m^2)$.

The blue circle here is $x^2 + y^2 = 25,$ while the green line is $y = mx + c$.

When a line and a circle touch, what can we say about their equations?

Hence or otherwise find the equations of the two tangents to this circle from the point $(2,11)$.

What else can we write down about $c$ and $m$ if we know a point on the line?