Geo4.19

From Example Problems
Jump to: navigation, search

Find the circle which passes through (4,-3),(-1,2) and has its centre on the line 3x+4y+1=0\,

Let the equation of the circle be

x^{2}+y^{2}+2gx+2fy+c=0\,

The point (4,-3) lies on the circle,hence

16+9+8g-6f+c=0\,

8g-6f+c=-25\,

Point (-1,2) lies on the circle

1+4-2g+4f+c=0\,

2g-4f-c=5\,

Also the centre lies on 3x+4y+1=0\,

Hence

-3g-4f+1=0\,

solving the first two equations,we get

10g-10f=-20\,

g-f=-2\,

Solving this and the last equation,

-7f+7=0\,

Value of f is 1, g=-1 and c=11

Equation of the circle is

x^{2}+y^{2}-2x+2y-11=0\,


Main page:Geometry:Circles