Find the equation of the line through the point `A(2,3)` and making an angle an angle of `45^0` with the `x-a xi s` . Also, determine the length of intercept on it between `Aa n d` the line `x+y+1=0.`

Explanation

Given that the equation of a line through A and making an angle of `45^@` with the x axis is

`=>(x−2)cos45​=(y−3)​/sin45` or `=> x - y + 1 = 0`

Suppose that
this line meets the line `x + y + 1 = 0` at P such that AP = r
Then the co-ordinates of P are given by

`=>(x−2)/cos45^@​=(y-3)sin45=r`

`⇒x=2+rcos45,y=3+rsin45`

`⇒x=2+r/sqrt(2)`

​and `y=3+r/sqrt(2)`

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