但只可以計交點的x-坐標，而對應的y-坐標則要 自行計算。
方程的形式: Ax + By = C 及 x2 + y2 + Dx + Ey + F = 0
| ( | A | x2 | + | B | x2 | ) | x-1 |
| ( | 2 | A | C | - | D | B | x2 |
| + | X | A | B | + | √ | ( | ( |
| D | B | x2 | - | X | A | B | - |
| 2 | A | C | ) | x2 | - | 4 | ( |
| A | x2 | + | B | x2 | ) | ( | C |
| x2 | + | X | C | B | + | Y | B |
| x2 | ) | ) | cos | ( | K | sin-1 | 1 |
| ) | ) | ( | cos | ( | K | sin-1 | 1 |
| ) | ) | x2 | ÷ | 2 | + | ( | sin |
| STO F1 | |||||||
| ( | K | sin-1 | 1 | ) | ) | x2 | ( |
| C | - | A | ANS | ) | ÷ | B | - |
| K | - | 1 | + | ( | K | + | 1 |
| ) | STO F2 | ||||||
例題: 求直線3x - y = 5 與圓 x2 + y2 - 8x - 4y + 15 = 0 的交點。
按 2ndF DEL (必要) 再按 RCL F1 RCL F2 ALGB 3 = 1 +/- = 5 = 8 +/- = 4 +/- = 15 =
(顯示x為3) = (顯示y為4) = (顯示x為2) = (顯示y為1)
所以交點為 (3,4) 及 (2,1)。
直線與圓形的交點(簡化版)
| ( | A | x2 | + | B | x2 | ) | x-1 |
| ( | 2 | A | C | - | D | B | x2 |
| + | X | A | B | + | ( | +/- | 1 |
| ) | yx | K | √ | ( | ( | D | B |
| x2 | - | X | A | B | - | 2 | A |
| C | ) | x2 | - | 4 | ( | A | x2 |
| + | B | x2 | ) | ( | C | x2 | + |
| X | C | B | + | Y | B | x2 | ) |
| ) | ) | ÷ | 2 | - | 1 | + | 1 |
| STO F1 或 F2 | |||||||
例題: 求直線3x – y = 5 與圓 x2 + y2 – 8x – 4y + 15 = 0 的交點。
按 2ndF DEL (必要) 再按 RCL F1 ALGB 3 = 1 +/- = 5 = 8 +/- = 4 +/- = 15 = (顯示3) =
(顯示2)
所以交點的x-坐標為3及2，所對應的y-坐標則要自行計算。
相關資料:
圓形的圓心及半徑 (Centre and radius of a circle)
圓心及半徑求圓方程 (Equation of circle by centre and radius)
直徑兩點求圓方程 (Equation of circle by 2 end-point of diameter)
已知斜率求圓的切線 (Tangent to Circle with given slope)
外點至圓的切線斜率 (Slope of tangent to circle from external point)
三點求圓方程 (應用內置聯立三元一次方程 ) (Equation of circle from three points)
