If ax^2+2hxy+by^2+2gx+2fy+c=0 represents a pa | vedclass

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

Question

(B) The general second-degree equation $ax^2+2hxy+by^2+2gx+2fy+c=0$ represents a pair of parallel lines if $h^2=ab$ and $bg^2=af^2$.From $h^2=ab$,we h

Vedclass · Accepted Answer

$\sqrt{\frac{a}{b}}$

Vedclass · Answer

(B) The general second-degree equation $ax^2+2hxy+by^2+2gx+2fy+c=0$ represents a pair of parallel lines if $h^2=ab$ and $bg^2=af^2$.From $h^2=ab$,we have $h=\sqrt{ab}$.From $bg^2=af^2$,we can write $\frac{g^2}{f^2}=\frac{a}{b}$.For parallel lines,the condition is $\frac{a}{h}=\frac{h}{b}=\frac{g}{f}$.Thus,$\frac{g^2}{f^2}=\frac{a^2}{h^2}=\frac{a^2}{ab}=\frac{a}{b}$.Also,for parallel lines,the distance between them is given by $2\sqrt{\frac{g^2-ac}{a(a+b)}} = 2\sqrt{\frac{f^2-bc}{b(a+b)}}$.This implies $\frac{g^2-ac}{a} = \frac{f^2-bc}{b}$.Therefore,$\frac{g^2-ac}{f^2-bc} = \frac{a}{b}$.Taking the square root on both sides,we get $\sqrt{\frac{g^2-ac}{f^2-bc}} = \sqrt{\frac{a}{b}}$.

If $ax^2+2hxy+by^2+2gx+2fy+c=0$ represents a pair of parallel lines,then $\sqrt{\frac{g^2-ac}{f^2-bc}}$ is equal to

Similar Questions

$A$ diatomic gas $\left(\gamma = \frac{7}{5}\right)$ is compressed adiabatically to a volume $\frac{V_i}{32}$,where $V_i$ is its initial volume. The initial temperature of the gas is $T_i$ in Kelvin and the final temperature is $xT_i$. The value of $x$ is:

$A$ bag contains $5$ black balls,$4$ white balls,and $3$ red balls. If a ball is selected at random,the probability that it is a black or red ball is

Two of the lines represented by the equation $a y^4+b x y^3+c x^2 y^2+d x^3 y+e x^4=0$ will be perpendicular,then

Which series possesses an inferior ovary?

The energy of an electromagnetic radiation is $19.875 \times 10^{-13} \ erg$. What is its wave number in $cm^{-1}$? $(h = 6.625 \times 10^{-27} \ erg \ sec, c = 3 \times 10^{10} \ cm \ sec^{-1})$

Vedclass Test Series

Exam Paper Generator

Online Exam Module