The distance between the lines represented by | vedclass

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

Question

(C) The given equation is $4x^2 + 4xy + y^2 - 6x - 3y - 4 = 0$. We can rewrite the quadratic part as $(2x + y)^2 - 3(2x + y) - 4 = 0$. Let $t = 2x + y

Vedclass · Accepted Answer

$\sqrt{5}$ units

Vedclass · Answer

(C) The given equation is $4x^2 + 4xy + y^2 - 6x - 3y - 4 = 0$. We can rewrite the quadratic part as $(2x + y)^2 - 3(2x + y) - 4 = 0$. Let $t = 2x + y$. Then the equation becomes $t^2 - 3t - 4 = 0$. Factoring the quadratic,we get $(t - 4)(t + 1) = 0$. This gives two lines: $2x + y - 4 = 0$ and $2x + y + 1 = 0$. These lines are parallel because their slopes are equal $(m = -2)$. The distance $d$ between two parallel lines $Ax + By + C_1 = 0$ and $Ax + By + C_2 = 0$ is given by $d = \frac{|C_1 - C_2|}{\sqrt{A^2 + B^2}}$. Here,$A = 2, B = 1, C_1 = -4, C_2 = 1$. $d = \frac{|-4 - 1|}{\sqrt{2^2 + 1^2}} = \frac{|-5|}{\sqrt{5}} = \frac{5}{\sqrt{5}} = \sqrt{5}$ units.

The distance between the lines represented by the equation $4x^2 + 4xy + y^2 - 6x - 3y - 4 = 0$ is

Similar Questions

The lines joining the points of intersection of the line $x + y = 1$ and the curve $x^2 + y^2 - 2y + \lambda = 0$ to the origin are perpendicular. Then the value of $\lambda$ is:

The equation $8x^2 + 8xy + 2y^2 + 26x + 13y + 15 = 0$ represents a pair of parallel straight lines. The distance between them is

The equation of the bisectors of the angles between the lines joining the origin to the points of intersection of the curve $x^2+xy+y^2+x+3y+1=0$ and the line $x+y+2=0$ is

The equation of the pair of straight lines joining the origin to the points of intersection of the curve $x^2 + y^2 = 4$ and the line $y - x = 2$ is

If $\theta$ is the acute angle between the lines joining the origin to the points of intersection of the curve $x^2+xy+y^2+x+3y+1=0$ and the straight line $x+y+2=0$,then $\cos \theta=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module