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Find the equations to the straight lines which pass through the point (h, k) and are inclined at angle tan-1 m to the straight line y = mx + c.

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Best answer

Given: 

equation passes through (h, k) and make an angle of tan-1 m with the line y = mx + c 

To find: 

equation of given line

Explanation: 

We know that the equations of two lines passing through a point x1,y1 and making an angleα with the given line y = m ’x + c are 

m’ = m so,

 y - y1\(\frac {m±\,tan\ \,\alpha}{1±m\,tan\ \,\alpha}\) (x - x1)

Here,x1 = h, y1 = k, α = tan-1 m’ = m. 

So, the equations of the required lines are

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