A local band sells out for their concert. They sell all 1,175 tickets for a total purse of $28,112.50. The tickets were priced a
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Step-by-step explanation:
The general equation of a circle is
,
where <em>h</em> and <em>k</em> forms the coordinates of the centre of the circle.
When the circle has a centre at the origin, the equation reduces into
. .
Now, we are interested in solving for the <em>x</em>-intercepts (the <em>x</em>-coordinates when the circle intersects the <em>x</em>-axis), of the circle
.
Thus,
.
Geometrically speaking, the tangent to the circle at the point defined by one of the <em>x</em>-intercepts of the circle is actually a vertical line, more specifically the lines .
First and foremost, for the vertical line , it intersects the straight line
, giving the y-coordinate for point P,
.
Hence, the coordinates of point P are .
However, since there are no boundaries given in the question and a circle is symmetrical about its centre, thus, point P also exists when the vertical line and interdects the straight line
.
.
Therefore, the coordinates of point P are also .