(a) the perpendicular bisector of the chord PQ contains the center of the circle. Since PQ has slope -3, the perpendicular will have slope 1/3. So, the line is
y-1 = 1/3 (x-2)
Similarly, the radius through Q is perpendicular to the line 2x-y=13. Its equation is
y+5 = -1/2 (x-4)
Those two lines intersect at the center of the circle.
Now just crank out the details.
Point P(2,1) and Q(4,-5) lie on a circle. If
line 2x-y-13=0 is a tangent to the circle at Q,
what is
(*) Coordinates of the center of the circle;
(*) Equation of the circle.
(*) Sketch out your circle.
Step
2 answers
I forgot that the perpendicular bisector passes through the midpoint of PQ: (3,-2). So, its equation is
y+2 = 1/3 (x-3)
So, the center of the circle is at (0,-3).
Now find the radius, and you're about done.
y+2 = 1/3 (x-3)
So, the center of the circle is at (0,-3).
Now find the radius, and you're about done.