r=5
Circle is tangent to the line 3x+4y=24 at (2, 41/2)
Or tangent is 3x+4y=24.
Slope of tangent =−43
Let the equation of the circle be (x−h)2+(y−k)2=r2
⇒(x−h)2+(y−k)2=52⇒(x−h)2+(y−k)2=25 ...(i)
On differentiating w.r.t x,
2(x−h)+2(y−k)y′=0⇒y′=y−kx−h [Slope of tangent]
For (2, 41/2), put x=2,y=41/2,y′=−3/4 in above equation.
−43=241−k2−h⇒h=−34k−88
There is no other info in the problem, as the question is incomplete.
Assume h=0, then k=22
Now put it in (i), we will get the equation of circle.
x2+(y−22)2=25
Comments