Let L be the line 2x + y = 2. If the axes are | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The equation of the line is $2x + y = 2$,which can be written in intercept form as $\frac{x}{1} + \frac{y}{2} = 1$. Here,the intercepts on the ori

Vedclass · Accepted Answer

$2\sqrt{2}/3$ and $-2\sqrt{2}$

Vedclass · Answer

(C) The equation of the line is $2x + y = 2$,which can be written in intercept form as $\frac{x}{1} + \frac{y}{2} = 1$. Here,the intercepts on the original axes are $a = 1$ and $b = 2$.When the axes are rotated by an angle $\alpha = 45^\circ$ in the anticlockwise direction,the new intercepts $p$ and $q$ are given by the formulas:$\frac{1}{p} = \frac{1}{a} \cos \alpha + \frac{1}{b} \sin \alpha$$\frac{1}{q} = -\frac{1}{a} \sin \alpha + \frac{1}{b} \cos \alpha$Substituting $a = 1$,$b = 2$,and $\alpha = 45^\circ$:$\frac{1}{p} = \frac{1}{1} \cdot \frac{1}{\sqrt{2}} + \frac{1}{2} \cdot \frac{1}{\sqrt{2}} = \frac{1}{\sqrt{2}} + \frac{1}{2\sqrt{2}} = \frac{3}{2\sqrt{2}}$ $\Rightarrow p = \frac{2\sqrt{2}}{3}$$\frac{1}{q} = -\frac{1}{1} \cdot \frac{1}{\sqrt{2}} + \frac{1}{2} \cdot \frac{1}{\sqrt{2}} = -\frac{1}{\sqrt{2}} + \frac{1}{2\sqrt{2}} = -\frac{1}{2\sqrt{2}}$ $\Rightarrow q = -2\sqrt{2}$Thus,the intercepts are $\frac{2\sqrt{2}}{3}$ and $-2\sqrt{2}$.

Let $L$ be the line $2x + y = 2$. If the axes are rotated by $45^\circ$,then the intercepts made by the line $L$ on the new axes are respectively

Similar Questions

The coordinates of the point $(3,-7,5)$ in the new system,when the origin is shifted to the point $(-1,-1,-1)$ by the translation of axes,are

$A$ line makes intercepts $5$ and $7$ on the coordinate axes. The axes are rotated through an angle $\theta$ in the positive direction about the origin so that the line makes equal intercepts on the new axes,then $|\tan \theta|=$

The transformed equation of $3x^2 - 4xy = r^2$ when the coordinate axes are rotated about the origin through an angle of $\operatorname{Tan}^{-1}(2)$ in the positive direction is:

The new coordinates of a point $(4, 5)$,when the origin is shifted to the point $(1, -2)$ are

If the coordinates of a point $P$ change to $(2, -6)$ when the coordinate axes are rotated through an angle of $135^{\circ}$,then the coordinates of $P$ in the original system are

Vedclass Test Series

Exam Paper Generator

Online Exam Module