How to find an equation of a circle?

[Rose34]

Can someone please help I do not know how to start.

Q1)Find the equation of the circle whose centre lies on the line y = 4 and which passes through the points (2,0) and (6,0).
Q2) Find the equations of the circles which touch the x-axis, have radius 5 and pass through the point (0,8).


Thanks in advance.

[S_R_K]

Can someone please help I do not know how to start.

Q1)Find the equation of the circle whose centre lies on the line y = 4 and which passes through the points (2,0) and (6,0).
Q2) Find the equations of the circles which touch the x-axis, have radius 5 and pass through the point (0,8).


Thanks in advance.

Drawing diagrams for these sorts of questions, and substituting what you know into an equation is always helpful.

For Q1, a circle with its centre at y=4 has equation (x-h)^2 + (y-4)^2=r^2. Then substituting in the two points gives two equations in h and r which can be solved simultaneously.

For Q2, for a circle which just touches an axis, the distance from the centre to the axis is equal to the radius. Hence we have (x-h)^2+(y-5)^2=25. Substitute in the point (0,8) and solve for h.

[Rose34]

Drawing diagrams for these sorts of questions, and substituting what you know into an equation is always helpful.

For Q1, a circle with its centre at y=4 has equation (x-h)^2 + (y-4)^2=r^2. Then substituting in the two points gives two equations in h and r which can be solved simultaneously.

For Q2, for a circle which just touches an axis, the distance from the centre to the axis is equal to the radius. Hence we have (x-h)^2+(y-5)^2=25. Substitute in the point (0,8) and solve for h.

Thank you so much!!