Find the distance between the lines 5x-12y+15=0 and 10x-24y=7
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5x-12y+15 = 0 ⇒10x-24y+30=0 ----1)
10x-24y-7=0 -------2)
1) and 2) are parallel
Here , c1=30 ,c2 = -7, a1 = 10, b1 = -24
Distance between parallel lines = [tex] \frac{c1-c2}{ \sqrt{a1^2+b1^2} } = \frac{37}{ \sqrt{100+576} } = \frac{37}{26} [/tex]
Distance between lines = 37/26 units
10x-24y-7=0 -------2)
1) and 2) are parallel
Here , c1=30 ,c2 = -7, a1 = 10, b1 = -24
Distance between parallel lines = [tex] \frac{c1-c2}{ \sqrt{a1^2+b1^2} } = \frac{37}{ \sqrt{100+576} } = \frac{37}{26} [/tex]
Distance between lines = 37/26 units
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