Question

A circle has its centre on the line 5 x - 2y +1 = 0 and cuts the x-axis at the two points whose abscissa are -5 and 3 find equation of the circle

Answer 1

Answer:

solved

Step-by-step explanation:

the circle  cuts the x-axis at the two points A ( -5,0) and B (3 ,0)

mid point of AB = ( -1,0) , slope of AB = 0 , slope of perpendicular bisector of AB is ±∞ ( it is parallel to the y-axis).

equation of the perpendicular bisector of AB is x = -1

solving with the line 5 x - 2y +1 = 0

x = -1 , y = 2 → (-1,2) is the center of the circle

equation of the circle is

(x+1)² + (y-2)² = 5²

x² + y² +2x -4y - 20 = 0