If a pair of lines drawn through the origin f | vedclass

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

Question

(A) The given line is $2x + 3y = 6$,which has a slope $m_1 = -2/3$. Since the pair of lines passing through the origin forms an isosceles right-angled

Vedclass · Accepted Answer

$x - 5y = 0, 5x + y = 0$

Vedclass · Answer

(A) The given line is $2x + 3y = 6$,which has a slope $m_1 = -2/3$. Since the pair of lines passing through the origin forms an isosceles right-angled triangle with this line,the lines must make an angle of $45^{\circ}$ with the given line. Let the slope of the required lines be $m$. The angle between the lines is given by $	an 	heta = |(m - m_1) / (1 + m \cdot m_1)|$. Setting $	heta = 45^{\circ}$ and $m_1 = -2/3$: $1 = |(m - (-2/3)) / (1 + m(-2/3))| = |(3m + 2) / (3 - 2m)|$. This gives two cases: Case $1$: $(3m + 2) / (3 - 2m) = 1$ $\Rightarrow 3m + 2 = 3 - 2m$ $\Rightarrow 5m = 1$ $\Rightarrow m = 1/5$. The equation of the line is $y = (1/5)x \Rightarrow x - 5y = 0$. Case $2$: $(3m + 2) / (3 - 2m) = -1$ $\Rightarrow 3m + 2 = -3 + 2m$ $\Rightarrow m = -5$. The equation of the line is $y = -5x \Rightarrow 5x + y = 0$. Thus,the lines are $x - 5y = 0$ and $5x + y = 0$.

If a pair of lines drawn through the origin forms an isosceles right-angled triangle with the line $2x + 3y = 6$,then those lines are

Similar Questions

The distance from the origin to the orthocentre of the triangle formed by the lines $x+y-1=0$ and $6x^2-13xy+5y^2=0$ is

The area (in sq units) of the quadrilateral formed by two pairs of lines $\lambda^2 x^2 - m^2 y^2 - n(\lambda x + my) = 0$ and $\lambda^2 x^2 - m^2 y^2 + n(\lambda x + my) = 0$ is:

If $2x^2-5xy+2y^2=0$ represents two sides of a triangle whose centroid is $(1,1)$,then the equation of the third side is

If the lines represented by $a x^2+2 h x y+b y^2+2 g x+2 f y+c=0$ intersect on the $x$-axis,which of the following is in general incorrect?

The pairs of straight lines $x^2-3xy+2y^2=0$ and $x^2-3xy+2y^2+x-2=0$ form a

Vedclass Test Series

Exam Paper Generator

Online Exam Module