The distance from a point (1, 1, 1) to a vari | vedclass

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

Question

(C) Let the equation of the plane $\pi$ be $\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1$,where $A = (a, 0, 0)$,$B = (0, b, 0)$,and $C = (0, 0, c)$.The

Vedclass · Accepted Answer

$\left(\frac{1}{x} + \frac{1}{y} + \frac{1}{z} - 1\right)^2 = 144\left(\frac{1}{x^2} + \frac{1}{y^2} + \frac{1}{z^2}\right)$

Vedclass · Answer

(C) Let the equation of the plane $\pi$ be $\frac{x}{a} + \frac{y}{b} + \frac{z}{c} = 1$,where $A = (a, 0, 0)$,$B = (0, b, 0)$,and $C = (0, 0, c)$.The distance from point $(1, 1, 1)$ to the plane $\frac{x}{a} + \frac{y}{b} + \frac{z}{c} - 1 = 0$ is given by $d = \frac{|\frac{1}{a} + \frac{1}{b} + \frac{1}{c} - 1|}{\sqrt{\frac{1}{a^2} + \frac{1}{b^2} + \frac{1}{c^2}}} = 12$.Squaring both sides,we get $\left(\frac{1}{a} + \frac{1}{b} + \frac{1}{c} - 1\right)^2 = 144\left(\frac{1}{a^2} + \frac{1}{b^2} + \frac{1}{c^2}\right)$.The point $P$ is the intersection of planes $x=a$,$y=b$,and $z=c$,so $P \equiv (a, b, c)$.Replacing $(a, b, c)$ with $(x, y, z)$,the locus of $P$ is $\left(\frac{1}{x} + \frac{1}{y} + \frac{1}{z} - 1\right)^2 = 144\left(\frac{1}{x^2} + \frac{1}{y^2} + \frac{1}{z^2}\right)$.

Similar Questions

Let $A (1, 3, 5)$ and $B (-2, 3, -4)$ be two points. If a point $P(x, y, z)$ moves such that $PA^2 - PB^2 = 6c$,find the locus of $P$.

Let the plane $x+3y-2z+6=0$ meet the coordinate axes at the points $A, B, C$. If the orthocentre of the triangle $ABC$ is $\left(\alpha, \beta, \frac{6}{7}\right)$,then $98(\alpha+\beta)^2$ is equal to $........$.

The locus represented by $xy + yz = 0$ is

The combined equation for a pair of planes is $S \equiv 2 x^2-6 y^2-12 z^2+18 y z+2 z x+x y=0$. If one of the planes is parallel to $x+2 y-2 z=5$,then the acute angle between the planes $S=0$ is

Find the equation of a plane that is at a unit distance from the origin and is parallel to the plane $x - 2y + 2z - 5 = 0$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module