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C2 Co-ordinate Geometry - Help!

Hey!
Not really sure where to begin with this q, if anybody could help me out i'd be so grateful :biggrin:

The line x=-2 is a tangent to the circle x^2 + y^2 - 6x - 10y + 9 = 0
find the coordinates of the point of contact.

Thank youuu :smile: x
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Ezraeil
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TwirlGirl
Hey!
Not really sure where to begin with this q, if anybody could help me out i'd be so grateful :biggrin:

The line x=-2 is a tangent to the circle x^2 + y^2 - 6x - 10y + 9 = 0
find the coordinates of the point of contact.

Thank youuu :smile: x


The line x=-2 is a point on the circle and so if you substitute x=-2 for x in the equation of the circle and multiply it out,you'll end up with a quadratic which can be solved for y.

So

(-2)^2+y^2 - (6*-2)-10y+9=0

4+y+12-10y+9=0

y-10y+25=0

Now solve this as you would a quadratic for y :smile:

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