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A circle has its centre on the straight line 5x-2+1=0 and cuts the x-axis at the two points wose abscissae are(-5)and 3 find the equation of the circle and its radius

Profile image of aradhya singh
9 Years agoGrade Select Grade
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1 Answer

Profile image of Vikas TU
9 Years ago
The staright line in the question ought to be 5x-2y+1=0 ( y is lost in the condition) 
Leave focus alone the circle be (h,k) 
Since fixate lies on straight, line 5x-2y+1=0 
5h - 2k +1 =0 
Since the circle cuts x-pivot at (- 5,0) and (3,0) 
(- 5-h)^2 + (0-k)^2 = (3-h)^2 + (0-k)^2 
16h = - 16 
h=-1 
Substituting h=-1 in straight line condition 2k = - 4 
k=-2 
Range is equivalent to 
(- 5-h)^2 + (0-k)^2 = r^2 
(- 5+1)^2 + (0+2)^2 = r^2 
r= 20 ^ ½ 
Condition of circle is 
(x+1)^2 + (y+2)^2 = 20 

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