If the equation ax^2 + by^2 + cx + cy = 0 rep | vedclass

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

Question

(C) The general equation of a second-degree curve is $Ax^2 + 2Hxy + By^2 + 2Gx + 2Fy + C = 0$.For this to represent a pair of straight lines,the condi

Vedclass · Accepted Answer

$c(a + b) = 0$

Vedclass · Answer

(C) The general equation of a second-degree curve is $Ax^2 + 2Hxy + By^2 + 2Gx + 2Fy + C = 0$.For this to represent a pair of straight lines,the condition is $ABC + 2FGH - AF^2 - BG^2 - CH^2 = 0$.Comparing $ax^2 + by^2 + cx + cy = 0$ with the general equation,we have:$A = a, B = b, C = 0, H = 0, G = c/2, F = c/2$.Substituting these values into the condition:$a(b)(0) + 2(c/2)(c/2)(0) - a(c/2)^2 - b(c/2)^2 - 0(0)^2 = 0$.This simplifies to:$-a(c^2/4) - b(c^2/4) = 0$.Multiplying by $-4$,we get:$ac^2 + bc^2 = 0$.$c^2(a + b) = 0$.Therefore,$c(a + b) = 0$.

If the equation $ax^2 + by^2 + cx + cy = 0$ represents a pair of straight lines,then

Similar Questions

The joint equation of the straight lines $x + y = 1$ and $x - y = 4$ is

If the angles made by the lines represented by the equation $ax^2 + 2hxy + by^2 = 0$ with the $X$-axis are $\alpha$ and $\beta$, then $\tan(\alpha + \beta)$ is

If the slope of one line of the pair of lines $2x^2 + hxy + 6y^2 = 0$ is thrice the slope of the other line,then $h =$

If $s$ and $p$ are respectively the sum and the product of the slopes of the lines $3x^2 - 2xy - 15y^2 = 0$,then $s:p$ is equal to

For what value of $k$ does the equation $kx^2 - 10xy + 12y^2 + 5x - 16y - 3 = 0$ represent a pair of straight lines?

Vedclass Test Series

Exam Paper Generator

Online Exam Module