If the products of the perpendiculars from th | vedclass

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

Question

(C) The product of the perpendiculars from the origin $(0,0)$ to the pair of lines represented by $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ is given by

Vedclass · Accepted Answer

$p_3 < p_2 < p_1$

Vedclass · Answer

(C) The product of the perpendiculars from the origin $(0,0)$ to the pair of lines represented by $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ is given by $p = \left| \frac{c}{\sqrt{(a-b)^2 + 4h^2}} \right|$.For $xy+x+y+1=0$:$a=0, b=0, h=1/2, c=1$.$p_1 = \left| \frac{1}{\sqrt{(0-0)^2 + 4(1/2)^2}} \right| = \left| \frac{1}{\sqrt{1}} \right| = 1$.For $x^2-y^2+2x+1=0$:$a=1, b=-1, h=0, c=1$.$p_2 = \left| \frac{1}{\sqrt{(1-(-1))^2 + 4(0)^2}} \right| = \left| \frac{1}{\sqrt{4}} \right| = 1/2$.For $2x^2+3xy-2y^2+2x+1=0$:$a=2, b=-2, h=3/2, c=1$.$p_3 = \left| \frac{1}{\sqrt{(2-(-2))^2 + 4(3/2)^2}} \right| = \left| \frac{1}{\sqrt{16 + 9}} \right| = \frac{1}{\sqrt{25}} = 1/5$.Comparing the values: $1/5 < 1/2 < 1$,which means $p_3 < p_2 < p_1$.

If the products of the perpendiculars from the origin to the pairs of lines $xy+x+y+1=0$,$x^2-y^2+2x+1=0$,and $2x^2+3xy-2y^2+2x+1=0$ are $p_1, p_2$,and $p_3$ respectively,then:

Similar Questions

If $\alpha x^2+2 \gamma x y+\beta y^2=0$ is the equation of a pair of lines passing through the origin and perpendicular to the pair of lines $b h x^2+a b x y+a h y^2=0$ $(a \neq 0, b \neq 0)$,then $\frac{\alpha \beta}{\gamma^2}=$

If the slope of one of the lines represented by $ax^2+2hxy+by^2=0$ is twice that of the other,then $h^2:ab$ is

The equation of the pair of straight lines perpendicular to the pair $ax^2 + 2hxy + by^2 = 0$ is

The joint equation of the pair of lines passing through the origin and forming an equilateral triangle with the line $x=3$ is

If $ax^2-34xy-5y^2+2x+26y-5=0$ represents a pair of straight lines,then the value of $a$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module