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Question
Find the angle between the pair of straight lines 3x2 – 5xy – 2y2 + 17x + y + 10 = 0.
Solution
The given equation is 3x2 – 5xy – 2y2 + 17x + y + 10 = 0
Here a = 3, 2h = -5, b = -2
If θ is the angle between the given straight lines then
θ = `tan^-1 [|(2sqrt("h"^2 - ab))/(a + b)|]`
`= tan^-1 [(2sqrt(((-5)/2)^2 - 3(-2)))/(3 + (- 2))]`
`= tan^-1 [|(2sqrt(25/4 + 6))/1|]`
`= tan^-1 [|2 sqrt((25 + 24)/4)|]`
`= tan^-1 [|2 xx sqrt(49/4)|]`
`= tan^-1 [|2xx7/2|]`
= tan-1 (7)
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