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Please help with this question

Hi everyone, can someone try and help me with this question on finding the equation of a tangent to a circle?

Question:
The circle C has equation x²+18x+y²-2y+29=0.
Find an equation for the tangent to C at the point P (-7,-6), giving your answer in the form y=mx+b.

Thanks in advance for help
So far I have got the centre of the circle as (-9,1) and the radius of the circle as the square root of 53.
That's all I have so far
Now you know the coordinates of the centre of the circle, are you able to find the gradient of the line going through the centre of the circle and through the point (-7,-6)?
Original post by confusedcornish
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In addition to what @Username939 has said,

I can show you it graphically,

You want to obtain the tangent at C which is the purple line in the diagram.

If you work out the gradient of the centre and point P, you have the line normal to the circle (look at the diagram, you can see the circle and the orange line are perpendicular to each other) but you want the tangent to the circle so you do −1m-\frac{1}{m} and you should be good from here.

graph.jpg

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