If straight lines alpha^2x + alpha y = 9 and | vedclass

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

Question

(A) The equation of the first line is $\alpha^2x + \alpha y = 9$,which can be written as $\alpha y = -\alpha^2x + 9$,or $y = -\alpha x + \frac{9}{\alp

Vedclass · Accepted Answer

$-2/3$

Vedclass · Answer

(A) The equation of the first line is $\alpha^2x + \alpha y = 9$,which can be written as $\alpha y = -\alpha^2x + 9$,or $y = -\alpha x + \frac{9}{\alpha}$. The slope $m_1$ is $-\alpha$.The equation of the second line is $3x + 2y = 5$,which can be written as $2y = -3x + 5$,or $y = -\frac{3}{2}x + \frac{5}{2}$. The slope $m_2$ is $-\frac{3}{2}$.Since the lines are perpendicular,the product of their slopes must be $-1$,so $m_1 	imes m_2 = -1$.Substituting the values,$(-\alpha) 	imes (-\frac{3}{2}) = -1$.$\frac{3}{2}\alpha = -1$.$\alpha = -\frac{2}{3}$.

If straight lines $\alpha^2x + \alpha y = 9$ and $3x + 2y = 5$ are perpendicular,then the value of $\alpha$ is

Similar Questions

If the lines $y = (2 + \sqrt{3})x + 4$ and $y = kx + 6$ are inclined at an angle of $60^{\circ}$ to each other,then the value of $k$ will be

Find the equation of the lines passing through the origin and making an angle of $tan^{-1} m$ with the line $y = mx + c$.

Two lines pass through the point $(2,3)$ and intersect each other at an angle of $60^{\circ}$. If the slope of one line is $2$,find the equations of the other line.

If $m_1$ and $m_2$ $(m_1 > m_2)$ are the slopes of the lines which make an angle of $30^{\circ}$ with the line joining the points $(1, 2)$ and $(3, 4)$,then $\frac{m_1}{m_2} = $

If the coordinates of the vertices $A, B, C$ of the triangle $ABC$ are $(-4, 2)$,$(12, -2)$,and $(8, 6)$ respectively,then $\angle B$ =

Vedclass Test Series

Exam Paper Generator

Online Exam Module