Straight Line

2013-01-22 3:54 pm

Straight Line L passes through point (1,1) and its distance from point (4,5) is 2 units. Find :
(1) Equation(s) of L.
(2) Point on L closest to (4,5).
Note : Using formula outside the DSE syllabus is not allowed.

回答 (3)

50418129

2013-01-22 5:30 pm

✔ 最佳答案

Let P(x, y) be the projection of (4, 5) on L

since L is perpendicular to the line joined P and (4,5),
[(y - 1)/(x - 1)] [(y - 5)/(x - 4)] = -1
(y - 1)(y - 5) = -(x - 1)(x - 4)
x² + y² - 5x - 6y + 9 = 0 ---------------------------------------------- (i)

since the distance from P to (4, 5) = 2
√[(x - 4)² + (y - 5)²] = 2
(x - 4)² + (y - 5)² = 4
x² + y² - 8x - 10y + 37 = 0 ----------------------------------------- (ii)

(i) - (ii), 3x + 4y - 28 = 0 => x = (28 - 4y)/3
substitute x = (28 - 4y)/3 into (i),
[(28 - 4y)/3]² + y² - 5[(28 - 4y)/3] - 6y + 9 = 0
(28 - 4y)² + 9y² - 15(28 - 4y) - 54y + 81 = 0
16y² - 224y + 784 + 9y² - 420 + 60y - 54y + 81 = 0
25y² - 218y + 445 = 0
y = (218 ± √3024) / 50 = (109 ± 6√21) / 25

I think you should know how to do next!!!

參考: knowledge

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明隆

2013-01-26 8:40 pm

good!!!!!!!!!!!!!

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Yiukai

2013-01-22 3:57 pm

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