If frac{x^2}{a} + frac{2xy}{h} + frac{y^2}{b} | vedclass

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

Question

(B) The given equation is $\frac{x^2}{a} + \frac{2xy}{h} + \frac{y^2}{b} = 0$. Multiplying by $abh$,we get $bhx^2 + 2abyx + ahy^2 = 0$. Comparing this

Vedclass · Accepted Answer

$9 : 8$

Vedclass · Answer

(B) The given equation is $\frac{x^2}{a} + \frac{2xy}{h} + \frac{y^2}{b} = 0$. Multiplying by $abh$,we get $bhx^2 + 2abyx + ahy^2 = 0$. Comparing this with the standard form $Ax^2 + 2Hxy + By^2 = 0$,we have $A = bh$,$2H = 2ab \Rightarrow H = ab$,and $B = ah$. Let the slopes be $m_1$ and $m_2$. We are given $m_2 = 2m_1$. For the equation $Ax^2 + 2Hxy + By^2 = 0$,the sum of slopes $m_1 + m_2 = -\frac{2H}{B}$ and the product of slopes $m_1 m_2 = \frac{A}{B}$. $m_1 + 2m_1 = 3m_1 = -\frac{2ab}{ah} = -\frac{2b}{h} \Rightarrow m_1 = -\frac{2b}{3h}$. $m_1(2m_1) = 2m_1^2 = \frac{bh}{ah} = \frac{b}{a} \Rightarrow 2\left(-\frac{2b}{3h}ight)^2 = \frac{b}{a}$. $2 	imes \frac{4b^2}{9h^2} = \frac{b}{a} \Rightarrow \frac{8b^2}{9h^2} = \frac{b}{a}$. Dividing both sides by $b$ (assuming $b 
eq 0$),we get $\frac{8b}{9h^2} = \frac{1}{a} \Rightarrow \frac{ab}{h^2} = \frac{9}{8}$.

If $\frac{x^2}{a} + \frac{2xy}{h} + \frac{y^2}{b} = 0$ represents a pair of straight lines and the slope of one of the lines is twice that of the other,then $ab : h^2$ is:

Similar Questions

If the equation $ax^{2}+2hxy+by^{2}+2gx+2fy=0$ has one line as the bisector of the angle between the coordinate axes,then

The equation $2x^{2}+5xy-12y^{2}=0$ represents a

For $l \in R$,the equation $(2 l-3) x^2+2 l x y-y^2=0$ represents a pair of lines

The equation $2x^2 + 7xy + 3y^2 + 8x + 14y + \lambda = 0$ represents a pair of straight lines when $\lambda = $

The equation $x^2 - 2\sqrt{3}xy + 2y^2 = 0$ represents two sides of a triangle. If the angle between them is $\frac{\pi}{3}$,then the perimeter of that triangle is

Vedclass Test Series

Exam Paper Generator

Online Exam Module