The product of the lengths of the perpendicul | vedclass

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

Question

(C) The equation of the hyperbola is $x^2-y^2=8$. The asymptotes of the hyperbola $x^2-y^2=a^2$ are given by $x^2-y^2=0$,which implies $x-y=0$ and $x+

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(C) The equation of the hyperbola is $x^2-y^2=8$. The asymptotes of the hyperbola $x^2-y^2=a^2$ are given by $x^2-y^2=0$,which implies $x-y=0$ and $x+y=0$. Let $P(x, y)$ be any point on the hyperbola. The length of the perpendicular from $P(x, y)$ to the line $x-y=0$ is $d_1 = \frac{|x-y|}{\sqrt{1^2+(-1)^2}} = \frac{|x-y|}{\sqrt{2}}$. The length of the perpendicular from $P(x, y)$ to the line $x+y=0$ is $d_2 = \frac{|x+y|}{\sqrt{1^2+1^2}} = \frac{|x+y|}{\sqrt{2}}$. The product of the lengths of the perpendiculars is $d_1 	imes d_2 = \frac{|x-y|}{\sqrt{2}} 	imes \frac{|x+y|}{\sqrt{2}} = \frac{|x^2-y^2|}{2}$. Since the point lies on the hyperbola $x^2-y^2=8$,we substitute the value: $\frac{8}{2} = 4$.

The product of the lengths of the perpendiculars from any point on the hyperbola $x^2-y^2=8$ to its asymptotes is

Similar Questions

If force $F$ is increasing with time and at $t=0, F=0$,where will slipping first start?

Ethanol,when reacted with $PCl_5$,gives $A$,$POCl_3$,and $HCl$. $A$ reacts with silver nitrite to form $B$ (major product) and $AgCl$. $A$ and $B$ are respectively:

The potential difference between the plates of a parallel plate capacitor is changing at the rate of $10^6\, V/s$. If the capacitance is $2\,\mu F$,the displacement current in the dielectric of the capacitor will be.....$A$

Eubacteria is an example of which domain?

$74.5 \ g$ of a metallic chloride contain $35.5 \ g$ of chlorine. The equivalent weight of the metal is

Vedclass Test Series

Exam Paper Generator

Online Exam Module