Find the equations of the circles satisfying the given conditions :
1)touches y axis at (0,?3) and passes through (-1,0)
2)touches the line 2x-3y-7=0 at (2,-1) and passes through (4,1)
3)touches the line 3x+y+3=0 at (-3,6) and tangent x+3y-7=0.

Dear student
Assuming in part 1) the point as 0,3Let (h,k) be centre of circle.Circle touches the y-axisSo, radius will be h.Equation of circlex-h2+(y-k)2=h2It touches the y-axis at 0,30-h2+(3-k)2=h2h2+(3-k)2=h2(3-k)2=03-k=0k=3It passes through the point -1,0So,-1-h2+(0-3)2=h21+h2+2h+3=h24+2h=0h=-2So, equation of circle is x+22+(y-3)2=(-2)2x+22+(y-3)2=4
For remaining queries we request you to post them in separate threads to have rapid assistance from our experts.

Regards

  • 5
What are you looking for?