The straight lines joining the origin to the | vedclass

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

Question

(A) To find the equation of the pair of lines joining the origin to the intersection points,we homogenize the equation of the curve $3x^2 + 4xy - 4x +

Vedclass · Accepted Answer

$\pi/2$

Vedclass · Answer

(A) To find the equation of the pair of lines joining the origin to the intersection points,we homogenize the equation of the curve $3x^2 + 4xy - 4x + 1 = 0$ using the line $2x + y = 1$ (i.e.,$2x + y = 1$).Substituting $1 = (2x + y)$ into the curve equation:$3x^2 + 4xy - 4x(2x + y) + (2x + y)^2 = 0$Expanding the terms:$3x^2 + 4xy - 8x^2 - 4xy + 4x^2 + 4xy + y^2 = 0$Simplifying the expression:$-x^2 + 4xy + y^2 = 0$ or $x^2 - 4xy - y^2 = 0$Comparing this with the general form $ax^2 + 2hxy + by^2 = 0$,we have $a = 1$,$2h = -4$ (so $h = -2$),and $b = -1$.The angle $	heta$ between the lines is given by $	an 	heta = \left| \frac{2\sqrt{h^2 - ab}}{a + b} ight|$.Since $a + b = 1 + (-1) = 0$,the denominator is $0$,which implies $	an 	heta = \infty$.Therefore,$	heta = \pi/2$,meaning the lines are perpendicular.

The straight lines joining the origin to the points of intersection of the line $2x + y = 1$ and the curve $3x^2 + 4xy - 4x + 1 = 0$ include an angle of:

Similar Questions

Two lines are given by the equation $x^2 - 4xy + 4y^2 + kx - 2ky = 0$. Find the value of $k$ such that the distance between them is $3$.

The lines joining the origin to the points of intersection of the line $y = mx + c$ and the circle $x^2 + y^2 = a^2$ will be mutually perpendicular,if

The distance between the lines represented by the equation $x^2 + 2\sqrt{3}xy + 3y^2 - 3x - 3\sqrt{3}y - 4 = 0$ is

If the distance between the lines represented by $(x - 2y)^2 + k(x - 2y) = 0$ is $3$ units and $k > 0$, then the equations of the lines are:

The angle between the lines joining the origin to the points of intersection of the line $x\sqrt{3} + y = 2$ and the curve $x^2 + y^2 = 4$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module