SOLUTION: for the equation x^2+y^2-2x-4y-11=0 a.) find the center (h,k) and radius r of the circle. b.)Graph the circle c.) find the intercepts if any

Algebra ->  Rational-functions -> SOLUTION: for the equation x^2+y^2-2x-4y-11=0 a.) find the center (h,k) and radius r of the circle. b.)Graph the circle c.) find the intercepts if any      Log On


   

Question 1066238: for the equation x^2+y^2-2x-4y-11=0
a.) find the center (h,k) and radius r of the circle.
b.)Graph the circle
c.) find the intercepts if any
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
When ( h,k ) is the center of the circle,
+%28+x+-+h+%29%5E2+%2B+%28+y+-+k+%29%5E2+=+r%5E2+
+x%5E2+-+2h%2Ax+%2B+h%5E2+%2B+y%5E2+-+2k%2Ay+%2B+k%5E2+-+r%5E2+=+0+
+x%5E2+%2B+y%5E2+-2h%2Ax+-+2k%2Ay+%2B+%28+h%5E2+%2B+k%5E2+-+r%5E2+%29+=+0+
Comparing this to the given equation:
(1) +2x+=+2h%2Ax+
(2) +4y+=+2k%2Ay+
(3) +-11+=+h%5E2+%2B+k%5E2+-+r%5E2+
------------------------------
(1) +2+=+2h+
(1) +h+=+1+
and
(2) +4+=+2k+
(2) +k+=+2+
and
+-11+=+1%5E2+%2B+2%5E2+-+r%5E2+
+r%5E2+=+11+%2B+1+%2B+4+
+r%5E2+=+16+
+r+=+4+
-----------------------------
The center is at ( h, k ) = ( 1, 2 )
------------------------------
The x-intercept is where +y+=+0+
+%28+x+-+h+%29%5E2+%2B+%28+y+-+k+%29%5E2+=+r%5E2+
+%28+x+-+1+%29%5E2+%2B+%28+0+-+2+%29%5E2+=+4%5E2+
+%28+x+-+1+%29%5E2+=+16+-+4+
+%28+x+-+1+%29%5E2+=+12+
+x+-+1+=+sqrt%2812%29+
+x+=+1+%2B+2%2Asqrt%283%29+
and
+x+=+1+-+2%2Asqrt%283%29+
Those are x-intercepts
-----------------------
The y-intercepts are where +x+=+0+
+%28+x+-+h+%29%5E2+%2B+%28+y+-+k+%29%5E2+=+r%5E2+
+%28+0+-+1+%29%5E2+%2B+%28+y+-+2+%29%5E2+=+4%5E2+
+1%5E2+%2B+%28+y+-+2+%29%5E2+=+16+
+%28+y+-+2+%29%5E2+=+16+-+1+
+%28+y+-+2+%29%5E2+=+15+
+y+-+2+=+sqrt%2815%29+
+y+=+2+%2B+sqrt%2815%29+
and
+y+=+2+-+sqrt%2815%29+
Those are y-intercepts
--------------------------
Here's the plot: