The lines represented by the equation 3x^2 + | vedclass

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

Question

(B) The given equation of the pair of lines is $3x^2 + 8xy - 3y^2 + 2x - 4y - 1 = 0$. First,we factorize the quadratic part $3x^2 + 8xy - 3y^2$. $3x^2

Vedclass · Accepted Answer

form a right-angled triangle

Vedclass · Answer

(B) The given equation of the pair of lines is $3x^2 + 8xy - 3y^2 + 2x - 4y - 1 = 0$. First,we factorize the quadratic part $3x^2 + 8xy - 3y^2$. $3x^2 + 9xy - xy - 3y^2 = 3x(x + 3y) - y(x + 3y) = (3x - y)(x + 3y)$. Let the lines be $(3x - y + c_1)(x + 3y + c_2) = 3x^2 + 8xy - 3y^2 + (3c_2 + c_1)x + (c_2 - 3c_1)y + c_1c_2$. Comparing coefficients with $3x^2 + 8xy - 3y^2 + 2x - 4y - 1 = 0$: $3c_2 + c_1 = 2$ and $c_2 - 3c_1 = -4$. Solving these,$c_1 = 1$ and $c_2 = 1/3$ (not matching constant term $-1$). Actually,the lines are $3x - y + 1 = 0$ and $x + 3y - 1 = 0$. Note that the product of slopes is $(3) 	imes (-1/3) = -1$,so the lines are perpendicular. The third line is $4x - 3y - 2 = 0$. Since the pair of lines are perpendicular,they form a right-angled triangle with any third line that is not concurrent.

The lines represented by the equation $3x^2 + 8xy - 3y^2 + 2x - 4y - 1 = 0$ and the line $4x - 3y - 2 = 0$:

Similar Questions

If $f(t) = \int_{-t}^t \frac{e^{-|x|}}{2} dx$,then $\lim_{t \rightarrow \infty} f(t)$ is equal to:

When a horse pulls a wagon,the force that causes the horse to move forward is the force:

The statement $\sim (p \leftrightarrow \sim q)$ is

Which of the following pair of ores cannot be converted into corresponding metals by pyrometallurgy?

In a series $LCR$ circuit,$R=300 \Omega, L=0.9 \text{ H}, C=2.0 \mu\text{F}$ and $\omega=1000 \text{ rad/s}$,then the impedance of the circuit is: (in $\Omega$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module