Asked by kishor
Find the equation of a circle with radius 4 units ,whose center lies on the line 13x+4y=32 and which touch the line 3x+4y+28= 0.
Answers
Answered by
Steve
One way is to find the point on 13x+4y=32 which is at a distance of 4 from the line 3x+4y=28.
Since the distance from (h,k) to ax+by+c=0 is
|ah+bk+c|/√(a^2+b^2)
and we know that k = (32-13h)/4, we have
|3h+32-13h+28|/5 = 4
|-10h+60| = 20
h = 4 or 8
so, k = -5 or -18
Check the graphs at
http://www.wolframalpha.com/input/?i=plot+y%3D%2832-13x%29%2F4%2Cy%3D%28-28-3x%29%2F4%2C%28x-4%29^2%2B%28y%2B5%29^2%3D16%2C%28x-8%29^2%2B%28y%2B18%29^2%3D16
Since the distance from (h,k) to ax+by+c=0 is
|ah+bk+c|/√(a^2+b^2)
and we know that k = (32-13h)/4, we have
|3h+32-13h+28|/5 = 4
|-10h+60| = 20
h = 4 or 8
so, k = -5 or -18
Check the graphs at
http://www.wolframalpha.com/input/?i=plot+y%3D%2832-13x%29%2F4%2Cy%3D%28-28-3x%29%2F4%2C%28x-4%29^2%2B%28y%2B5%29^2%3D16%2C%28x-8%29^2%2B%28y%2B18%29^2%3D16
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.