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Sink41
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Doing a core 2 maths question, realized i can't remember how to find where a tangient and circle meet.
The circle equation provided in question was x^2 + y^2 -10x + 9 = 0
same as (x - 5)^2 + y^2 = 4^2
Question was:
"Given that line l with gradient 7/2 is a tangient to the circle, and that l touches circle at point T
find an equation that passes through the centre of the circle and T"
i tried to find out where line and circle met but wasnt able too. In mark scheme they had a very easy way to do it (m1m2=-1 so gradient is -2/7 and you know the co-ordinates of the centre of the circle, so you use y-y1 = m(x-x1) )
So, anyway i tried to put line and circle together and realized i couldnt... this is what i did how do you do it?
What i first was say that the forumula of the straight line is 7/2x + c = y where c is a constant
i then substituted that in the circle forumula to get (x-5)^2 + (7/2x + c)^2 = 4^2
multiplied out to get (53/4)x^2 + (7c - 10)x + 9 + c^2 = 0
since there can only be one result, b^2 - 4ac = 0 so
(7c -10)^2 - 4 * (53/4) * (9 + c^2) = 0
which ends up with
102c^2 -140c + 577 = 0
which does not have a result...
The circle equation provided in question was x^2 + y^2 -10x + 9 = 0
same as (x - 5)^2 + y^2 = 4^2
Question was:
"Given that line l with gradient 7/2 is a tangient to the circle, and that l touches circle at point T
find an equation that passes through the centre of the circle and T"
i tried to find out where line and circle met but wasnt able too. In mark scheme they had a very easy way to do it (m1m2=-1 so gradient is -2/7 and you know the co-ordinates of the centre of the circle, so you use y-y1 = m(x-x1) )
So, anyway i tried to put line and circle together and realized i couldnt... this is what i did how do you do it?
What i first was say that the forumula of the straight line is 7/2x + c = y where c is a constant
i then substituted that in the circle forumula to get (x-5)^2 + (7/2x + c)^2 = 4^2
multiplied out to get (53/4)x^2 + (7c - 10)x + 9 + c^2 = 0
since there can only be one result, b^2 - 4ac = 0 so
(7c -10)^2 - 4 * (53/4) * (9 + c^2) = 0
which ends up with
102c^2 -140c + 577 = 0
which does not have a result...