if the area of triangle with vertices ( 2a,a) (a,a) (a,2a)is 18 square units then the circumcenter of the triangle is
Answers
Answer:
Step-by-step explanation:
We want the equation of the circle which passes through the points (−3,4),(−3,4), (3,4),(3,4), and (−4,3).(−4,3).
The equation of a circle is x2+y2+ax+by+c=0.x2+y2+ax+by+c=0.
From the coordinates of the three given points we get following three equations:
(−3)2+42−3a+4b+c=0(−3)2+42−3a+4b+c=0
32+42+3a+4b+c=032+42+3a+4b+c=0
(−4)2+32−4a+3b+c=0(−4)2+32−4a+3b+c=0
We can simplify the above equations, and put them in matrix form:
⎡⎣⎢−33−4443111⎤⎦⎥⎡⎣⎢abc⎤⎦⎥=⎡⎣⎢−25−25−25⎤⎦⎥[−341341−431][abc]=[−25−25−25]
Solving the above matrix equation using Cramer's method, we get a=0,a=0, b=0,b=0, c=−25.c=−25.
Plugging in these values of a,a, b,b, and cc into the general form of the equation, we can now write the equation of the required circle as
x2+y2−25=0,x2+y2−25=0,
Or, expressing it in center radius form,
(x+0)2+(y+0)2=25(x+0)2+(y+0)2=25
The center of the circle is (0,0)(0,0) and the radius of the circle is 5.5.
The area of a circle with radius 55 is πr2πr2 == 25π