If the equation hxy + gx + fy + c = 0 represe | vedclass

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

Question

(B) The general equation of a second-degree curve is $ax^2 + by^2 + 2hxy + 2gx + 2fy + c = 0$. For this to represent a pair of straight lines,the cond

Vedclass · Accepted Answer

$fg = ch$

Vedclass · Answer

(B) The general equation of a second-degree curve is $ax^2 + by^2 + 2hxy + 2gx + 2fy + c = 0$. For this to represent a pair of straight lines,the condition is $abc + 2fgh - af^2 - bg^2 - ch^2 = 0$. Comparing the given equation $hxy + gx + fy + c = 0$ with the general form,we have $a = 0, b = 0, h' = h/2, g = g/2, f = f/2, c = c$. Substituting these values into the condition: $0(0)(c) + 2(f/2)(g/2)(h/2) - 0(f/2)^2 - 0(g/2)^2 - c(h/2)^2 = 0$. This simplifies to $\frac{fgh}{4} - \frac{ch^2}{4} = 0$. Multiplying by $4$,we get $fgh - ch^2 = 0$,which implies $h(fg - ch) = 0$. Since $h 
eq 0$ for the $xy$ term to exist,we must have $fg = ch$.

If the equation $hxy + gx + fy + c = 0$ represents a pair of straight lines,then

Similar Questions

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

The equations of the lines represented by the equation $ax^2 + (a + b)xy + by^2 + x + y = 0$ are

If the slope of one of the lines given by $ax^2 + 2hxy + by^2 = 0$ is $5$ times the other,then

If two lines represented by $ax^2+2hxy+by^2=0$ make angles $\alpha$ and $\beta$ with the positive direction of the $X$-axis,then $\tan(\alpha+\beta)=$

The equation of the pair of lines passing through the origin whose sum and product of slopes are respectively the arithmetic mean and geometric mean of $4$ and $9$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module