jee-advanced 2005 Q9

jee-advanced · India · screening Vectors 3D & Lines Triangle Properties and Special Points

9. A variable plane $x / a + y / b + z / c = 1$ at a unit distance from origin cuts the coordinate axes at $A , B$ and $C$. Centroid $( x , y , z )$ satisfies the equation $1 / x ^ { 2 } + 1 / y ^ { 2 } + 1 / z ^ { 2 } = K$. The value of $K$ is :
(a) 9
(b) 3
(c) $1 / 9$
(d) $1 / 3$

The locus of the centre of a circle which touches the $x$-axis and also externally touches the circle $x ^ { 2 } + ( y - 1 ) ^ { 2 } = 1$ is

9. A variable plane $x / a + y / b + z / c = 1$ at a unit distance from origin cuts the coordinate axes at $A , B$ and $C$. Centroid $( x , y , z )$ satisfies the equation $1 / x ^ { 2 } + 1 / y ^ { 2 } + 1 / z ^ { 2 } = K$. The value of $K$ is :\\
(a) 9\\
(b) 3\\
(c) $1 / 9$\\
(d) $1 / 3$\\

Paper Questions

Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q23 Q24 Q25 Q26 Q27 Q28