If a straight line is at a distance of 10 uni | vedclass

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

Question

(D) The normal form of a line is given by $x \cos \alpha + y \sin \alpha = p$,where $p$ is the perpendicular distance from the origin and $\alpha$ is

Vedclass · Accepted Answer

$x-y+10 \sqrt{2}=0$

Vedclass · Answer

(D) The normal form of a line is given by $x \cos \alpha + y \sin \alpha = p$,where $p$ is the perpendicular distance from the origin and $\alpha$ is the angle the normal makes with the positive $X$-axis.Given $p = 10$.The normal makes an angle of $\frac{\pi}{4}$ with the negative $X$-axis in the negative direction (clockwise).The negative $X$-axis corresponds to an angle of $\pi$.Moving $\frac{\pi}{4}$ in the negative direction (clockwise) from $\pi$ gives $\alpha = \pi - \frac{\pi}{4} = \frac{3\pi}{4}$.Substituting these values into the normal form equation:$x \cos(\frac{3\pi}{4}) + y \sin(\frac{3\pi}{4}) = 10$$x(-\frac{1}{\sqrt{2}}) + y(\frac{1}{\sqrt{2}}) = 10$$-x + y = 10\sqrt{2}$$x - y + 10\sqrt{2} = 0$.

If a straight line is at a distance of $10$ units from the origin and the perpendicular drawn from the origin to it makes an angle of $\frac{\pi}{4}$ with the negative $X$-axis in the negative direction,then the equation of that line is:

Similar Questions

$A$ ray of light coming from the point $(2, 2\sqrt{3})$ is incident at an angle $30^{\circ}$ with the normal to the line $x=1$ at the point $A$. The ray gets reflected on the line $x=1$ and meets the $x$-axis at the point $B$. Then,the line $AB$ passes through the point

Find the coordinates of the point where the line $3x - 2y - 6 = 0$ intersects the $Y$-axis.

Find the ratio in which the line joining points $A(-1, -1)$ and $B(2, 1)$ divides the line segment joining points $C(3, 4)$ and $D(1, 2)$.

Find the equation of the line passing through the point $(-2, 3)$ with a slope of $-4$.

Find the equation of the line perpendicular to the line $x-7y+5=0$ and having $x$-intercept $3$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module