UPSC NDA Math Model Paper 4

Here, we have to find the equation of the line whose inclination is 5π/6 and which makes an intercept of 6 units on the negative direction of the y-axis
As we know that, equation of a line whose slope is m and which makes an intercept c on the Y-axis is given by: y = mx + c
Here, we have c=−6 and m=tan(

5π

6

)=tan(π−

π

6

) =−tan‌

π

6

=−

1

√3

So, the equation of the required line is: y=−

1

√3

×x−6
⇒√3y=−x−6√3
So, the equation of the required line is x+√3y+6√3=0
Hence, option A is the correct answer.