The equations of the two straight lines passi | vedclass

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

Question

(B) The slope of the given line $x - 2y = 3$ is $m_1 = \frac{1}{2}$.Let the slope of the required lines be $m$.The angle between the lines is $45^{\ci

Vedclass · Accepted Answer

$3x - y - 7 = 0$ and $x + 3y - 9 = 0$

Vedclass · Answer

(B) The slope of the given line $x - 2y = 3$ is $m_1 = \frac{1}{2}$.Let the slope of the required lines be $m$.The angle between the lines is $45^{\circ}$,so $	an 45^{\circ} = \left| \frac{m - m_1}{1 + m \cdot m_1} ight|$.$1 = \left| \frac{m - 1/2}{1 + m/2} ight| = \left| \frac{2m - 1}{2 + m} ight|$.This gives two cases: $2m - 1 = m + 2$ or $2m - 1 = -(m + 2)$.Case $1$: $m = 3$. The equation is $y - 2 = 3(x - 3)$ $\Rightarrow y - 2 = 3x - 9$ $\Rightarrow 3x - y - 7 = 0$.Case $2$: $2m - 1 = -m - 2$ $\Rightarrow 3m = -1$ $\Rightarrow m = -1/3$. The equation is $y - 2 = -\frac{1}{3}(x - 3)$ $\Rightarrow 3y - 6 = -x + 3$ $\Rightarrow x + 3y - 9 = 0$.Thus,the equations are $3x - y - 7 = 0$ and $x + 3y - 9 = 0$.

The equations of the two straight lines passing through the point $(3, 2)$ and making an angle of $45^{\circ}$ with the line $x - 2y = 3$ are:

Similar Questions

The slope of a line $L$ is $2$. If $m_1$ and $m_2$ are the slopes of two lines which are inclined at an angle of $\frac{\pi}{6}$ with $L$,then $m_1 + m_2 =$

If a straight line $L$ passing through the point $(5, -3)$ is inclined at an angle of $60^{\circ}$ to the line $\sqrt{3}x + y - 9 = 0$ and $L$ intersects the $X$-axis,then the equation of $L$ is

If the line segment joining the points $(5, 2)$ and $(2, a)$ subtends an angle $\frac{\pi}{4}$ at the origin,then the absolute value of the product of all possible values of $a$ is:

$A$ line $L$ passes through the point $(3, -2)$ and is inclined at an angle of $60^{\circ}$ to the line $\sqrt{3}x + y = 1$. If $L$ also intersects the $x$-axis,then the equation of $L$ is:

If the straight lines $2x + 3y - 3 = 0$ and $x + ky + 7 = 0$ are perpendicular,then the value of $k$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module