The point p (7,-14) lies on the circle with equation x^2 + y^2 + 6x - 14y = 483. the point q also lies on the circle such that pq is a diameter. find the coordinates of point q.

ANSWER

P has coordinates


EXPLANATION

We need to first of all get the centre of the circle.

So let us complete the squares as follows,











We compare this to the general equation of the circle



This implies that, the center of the circle is



Let the coordinates of Q be


Since PQ is a diameter,the centre is the midpoint of PQ.

We now use the midpoint formula,



This implies that,



This implies












Therefore the coordinates of Q are

6(2x + 5y)6 (2x) = 12x6 (5y) = 30y12x + 30y

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