Question 1140775: (1) A cirlce is defined by the equation x^2-6x+y^2-2y=6.
(a) Rewrite the equation of the circle in the form:(x-a)^2+(y-b)^2=r^2
(b) Write down the coordinates of M,the centre of the circle.
(c) A tangent PQ is drawn from the point P(6;-2) to the circle, with Q the point of contact.Calculate the length of the tangent PQ.
Please can someone please help me with the question I begg
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website! (1) A cirlce is defined by the equation  .
(a) Rewrite the equation of the circle in the form:
 ............complete square
 ....... for  part is  and for  part is 
(b) Write down the coordinates of M,the centre of the circle.
since  and  ,
the coordinates of M are: ( ,)=( , )
(c) A tangent PQ is drawn from the point P( ; ) to the circle, with  the point of contact.Calculate the length of the tangent  .
if is a tangent, it is perpendicular to the radius
points  ,, and  form right triangle where  is hypotenuse,  and are legs
we can find the length of  using points P(;) and M(,)
 ->one leg
and
, the other leg will be:
P(;) and Q(,)
then we can find hypotenuse :
(,) and (,)
using Pythagorean theorem:
 .............=>so point ( ,)
then substitute in Pythagorean theorem:
 ........solve for
and, then
 =>
so ( , )
the length of the tangent is: distance between
(;)
(,)
double check:
tangent is a line passing through points P(;) and (,), so find equation
first find a slope:
and use slope point formula
 -> tangent line
line that passes through  and is perpendicular to tangent and it is:
and use slope point formula
Answer by greenestamps(13200)  (Show Source):
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