The area of the triangle formed by the lines | vedclass

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

Question

(C) The given equation is $y^2 - 9xy + 18x^2 = 0$. Factoring the quadratic equation,we get $(y - 3x)(y - 6x) = 0$. Thus,the two lines represented by t

Vedclass · Accepted Answer

$\frac{27}{4}$ sq. units

Vedclass · Answer

(C) The given equation is $y^2 - 9xy + 18x^2 = 0$. Factoring the quadratic equation,we get $(y - 3x)(y - 6x) = 0$. Thus,the two lines represented by the equation are $y = 3x$ and $y = 6x$. The third line is $y = 9$. To find the vertices of the triangle,we find the intersection points: $1$. Intersection of $y = 3x$ and $y = 6x$ is $(0, 0)$. $2$. Intersection of $y = 3x$ and $y = 9$ is $(3, 9)$. $3$. Intersection of $y = 6x$ and $y = 9$ is $(\frac{3}{2}, 9)$. The area of the triangle with vertices $(x_1, y_1), (x_2, y_2), (x_3, y_3)$ is given by $\frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$. Area $= \frac{1}{2} |0(9 - 9) + 3(9 - 0) + \frac{3}{2}(0 - 9)|$ Area $= \frac{1}{2} |0 + 27 - \frac{27}{2}| = \frac{1}{2} |\frac{54 - 27}{2}| = \frac{1}{2} 	imes \frac{27}{2} = \frac{27}{4}$ sq. units.

The area of the triangle formed by the lines $y^2 - 9xy + 18x^2 = 0$ and $y = 9$ is

Similar Questions

The lines represented by the equations $23x^2 - 48xy + 3y^2 = 0$ and $2x + 3y + 4 = 0$ form

The centroid of the triangle formed by the lines $x+y=1$ and $2y^2-xy-6x^2=0$ is

The equations to a pair of opposite sides of a parallelogram are $x^2 - 5x + 6 = 0$ and $y^2 - 6y + 5 = 0$. The equations to its diagonals are

If the lines represented by $2x^2 + 6xy + y^2 = 0$ are $L_1$ and $L_2$,and the lines represented by $4x^2 + 18xy + y^2 = 0$ are $l_1$ and $l_2$,and the acute angle between $L_1$ and $l_1$ is $\theta$,then the acute angle between $L_2$ and $l_2$ is :-

Suppose the slopes $m_1$ and $m_2$ of the lines represented by $ax^2+2hxy+by^2=0$ satisfy $3(m_1-m_2)-7=0$ and $m_1m_2-2=0$. Then,which of the following is true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module