If the equation given by hxy + 10x + 6y + 4 = | 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 $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$.Comparing $hxy + 10x + 6y + 4 = 0$ with the general form

Vedclass · Accepted Answer

$30$

Vedclass · Answer

(B) The general equation of a second-degree curve is $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$.Comparing $hxy + 10x + 6y + 4 = 0$ with the general form,we get $a = 0, b = 0, 2h' = h \Rightarrow h' = h/2, g = 5, f = 3, c = 4$.For the equation to represent a pair of lines,the determinant must be zero:$\Delta = \begin{vmatrix} a & h' & g \ h' & b & f \ g & f & c \end{vmatrix} = 0$$\begin{vmatrix} 0 & h/2 & 5 \ h/2 & 0 & 3 \ 5 & 3 & 4 \end{vmatrix} = 0$$0(0 - 9) - \frac{h}{2}(2h/2 - 15) + 5(3h/2 - 0) = 0$$-\frac{h}{2}(h - 15) + \frac{15h}{2} = 0$$-\frac{h^2}{2} + \frac{15h}{2} + \frac{15h}{2} = 0$$-\frac{h^2}{2} + 15h = 0$$-h^2 + 30h = 0 \Rightarrow h(30 - h) = 0$Therefore,$h = 0$ or $h = 30$.

If the equation given by $hxy + 10x + 6y + 4 = 0$ represents a pair of lines,then $h$ is equal to

Similar Questions

The value of $\lambda$, for which the equation $x^2 - y^2 - x - \lambda y - 2 = 0$ represents a pair of straight lines, is

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

Angles made by the lines represented by the equation $xy + y = 0$ with the $y$-axis are

If the equation $kxy + 10x + 8y + 16 = 0$ represents a pair of lines,then

The equation $x^3 + 8y^3 + 24xy = 64$ represents:

Vedclass Test Series

Exam Paper Generator

Online Exam Module