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What am I doing wrong? Finding a tangent to a circle

Hey guys.

So, I have the circle (x-5)^2 + (y-6)^2 = 9. I have to find an equation to a line that is a tangent to the circle but isn't vertical or horizontal.

I picked the point (3,8.236) which I solved by substituting x into the equation and finding y.

I worked out the equation of the line passing through (3,8.236) and the centre (5,6) and got y=-559/550x + 1159/100

Then I used the negative reciprocal of the gradient (550/559) and used the equation y-3=550/550(x-8.236) and got

y= 550/559x + 5.284300537 (calc gives this exact number)

After I put it into desmos, I my equation is somehow wrong and my passes through the circle by a fraction, has 2 'intersects' and is not an exact tangent.

What am I doing wrong? Thanks.

https://gyazo.com/585c39f826a277362e88b466606ca28b

Reply 1

Zacken

How did you "pick" that point?

Reply 2

username2975726

Original post by Zacken

How did you "pick" that point?

I knew the x points went from the points 2-8 because the radius is 3 with centre 5. If i picked x=2 then it would have been a vertical tangent which wasn't allowed, so i picked x=3 and put it into (3-5)^2 + (y-6)^2 = 9.