Question

The equation of the line which cuts off the intercepts $2\mathrm{a}\sec \left(\mathrm{\theta }\right)$ and $2\mathrm{a}cosec\left(\mathrm{\theta }\right)$ on the axes is

• A. $\mathrm{x}\sin \left(\mathrm{\theta }\right)+\mathrm{y}\cos \left(\mathrm{\theta }\right)–2\mathrm{a}=0$
• B. $\mathrm{x}\cos \left(\mathrm{\theta }\right)+\mathrm{y}\sin \left(\mathrm{\theta }\right)–2\mathrm{a}=0$
• C. $\mathrm{x}\sec \left(\mathrm{\theta }\right)+\mathrm{y}cosec\left(\mathrm{\theta }\right)–2\mathrm{a}=0$
• D. $\mathrm{x}\csc \left(\mathrm{\theta }\right)+\mathrm{y}\sec \left(\mathrm{\theta }\right)-2\mathrm{a}=0$

Answer 1

The correct option is B

$\mathrm{x}\cos \left(\mathrm{\theta }\right)+\mathrm{y}\sin \left(\mathrm{\theta }\right)–2\mathrm{a}=0$

Explanation of the correct option.

Given: $\mathrm{m}=2\mathrm{a}\sec \left(\mathrm{\theta }\right)$ and $\mathrm{n}=2\mathrm{a}cosec\left(\mathrm{\theta }\right)$

We know that equation of the line in intercept form is given by $\frac{\mathrm{x}}{\mathrm{m}}+\frac{\mathrm{y}}{\mathrm{n}}=1$.

Therefore, the equation of the given line is ,

$\frac{\mathrm{x}}{2\mathrm{a}\sec \left(\mathrm{\theta }\right)}+\frac{\mathrm{y}}{2\mathrm{a}cosec\left(\mathrm{\theta }\right)}=1$

$\Rightarrow$ $\mathrm{x}\cos \left(\mathrm{\theta }\right)+\mathrm{y}\sin \left(\mathrm{\theta }\right)=2\mathrm{a}$

$\Rightarrow$$\mathrm{x}\cos \left(\mathrm{\theta }\right)+\mathrm{y}\sin \left(\mathrm{\theta }\right)-2\mathrm{a}=0$

Hence, option $\left(B\right)$ is the correct answer.