These questions involve lengthy calculations. I have a vague idea of how to determine "h" and "k", but when it comes time to solve the quadratic, the roots never come out right. I am anxious to master coordinate geometry, but these problems have been significantly hindering my progress. Some help would be appreciated.
1. Find the equation of the circle passing through (2,1), tangent to the line 2x + y + 4 = 0 at (-1,-2). (Answer: (x-1)^2 + (y+1)^2 = 5)
2. Circles are drawn tangent to the line 3x + 4y - 6 = 0 at (6,-3). Their radii are equal to 7. Find their equations. (No answer given).
3. A circle having a radius of sqrt(17) passes through (-1,0), and is tangent to x+4y+10=0. Find its equation. (Answer: (x-3)^2 + (y-1)^2 = 17)
4. Find the equation of the circle which is tangent to the circle x^2 + y^2 - 12x - 2y + 32 = 0 at (5,3), and which passes through (-3,1). (Answer: (x+7/2)^2 + (y-20)^2 = 1445/4)
5.Circles passing through (8,4) and (6,6) are drawn tangent to the circle (x-2)^2 + (y-1)^2 = 9. Find their equations. (One Answer: (x-6)^2 + (y-4)^2 = 4)
1. Find the equation of the circle passing through (2,1), tangent to the line 2x + y + 4 = 0 at (-1,-2). (Answer: (x-1)^2 + (y+1)^2 = 5)
2. Circles are drawn tangent to the line 3x + 4y - 6 = 0 at (6,-3). Their radii are equal to 7. Find their equations. (No answer given).
3. A circle having a radius of sqrt(17) passes through (-1,0), and is tangent to x+4y+10=0. Find its equation. (Answer: (x-3)^2 + (y-1)^2 = 17)
4. Find the equation of the circle which is tangent to the circle x^2 + y^2 - 12x - 2y + 32 = 0 at (5,3), and which passes through (-3,1). (Answer: (x+7/2)^2 + (y-20)^2 = 1445/4)
5.Circles passing through (8,4) and (6,6) are drawn tangent to the circle (x-2)^2 + (y-1)^2 = 9. Find their equations. (One Answer: (x-6)^2 + (y-4)^2 = 4)