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Kelompok 5

It's talk about equation the circle with circle and line with line

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Kelompok 5

  1. 1. If a circle have an equation of circle : And a line have an equation of line : x 2 + y 2 + Ax + By + C = 0 Y = mx + n
  2. 2. Suppose that a line with equation of line y = mx + n and a circle with equation of x 2 + y 2 + Ax + By + C = 0 , then substitute the line’s equation into the circle’s equation to produce a new equation in the form of quadratic equation like above : x 2 + (mx + n) 2 + Ax + B (mx + n) + C = 0 x 2 + (m 2 x 2 + 2mnx + n 2 ) + Ax + B mx +Bn + C = 0 x 2 + m 2 x 2 + 2mnx + Ax + Bmx + n 2 + Bn + C = 0 (1 + m 2 ) x 2 + (2mn + A + Bm)x + n 2 + Bn + C = 0 Atau (1 + m 2 ) x 2 + (A + 2mn + B m )x + n 2 + Bn + C = 0
  3. 3. So , we can determine the simple form of the quadratic equation like above : <ul><li>And the value of discriminant is : </li></ul>ax 2 + bx + c = 0 D = b 2 – 4 . a . c <ul><li>According to above description, the requirement related to particular line’s position toward circle could be express as follow : </li></ul><ul><li>If D > 0 , so the line and circle have two intersection points </li></ul><ul><li>If D = 0 , so the line and circle have one intersection point </li></ul><ul><li>If D < 0 , so the line and circle have no intersection point </li></ul>
  4. 4. The line and circle have two intersection points The line and circle have an exactly one intersection point The line and circle have no intersection point

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