Guys how do you solve the following questions.
Find the equation of the circle with centre (2,-3) which touches the x axis.
Fidn the equation of the circle which touch the x axis, have radius 5 and pass through the point(0,8)
Thanks guys
For the first question, you know the coordinates of the centre you just need to determine the radius. Since the centre is three unit below the x axis, for it to only touch the x axis, the radius would be 3.
So your equation would be (x-2)
2+(y+3)
2=3
2The second question is a bit harder though.
Since you know it has a radius of 5 and touches the x axis, you know the centre is either 5 units above the x axis or 5 units below the x axis. But since it passes through the point (0,8) you can deduce that it is above the x axis.
So you know the centre of the circle has a y coordinate of 5 and a radius of 5 and passes through the point (0,8). Because it is a circle, the distance from the centre to any point on the circle will be the radius. So you know the distance from the centre to the point (0,8) will be 5.
Let a be the x coordinate of the centre, giving you the two points (a,5) and (0,8). Using the distance formula this gives you:
This gives two circles which have centres of (-4,5) and (4,5), giving you two equations;
(x-4)
2+(y-5)
2=5
2 or
(x+4)
2+(y-5)
2=5
2Hope this helps