Home
Class 11
MATHS
A point P moves on the fixed plane (x)/(...

A point P moves on the fixed plane `(x)/(a)+(y)/(b)+(z)/(c )=1` the plane through the point P and perpendicular to the line `bar(OP)` where `O=(0,0,0)` meets coordinate axes in A, B, C. Show that the locus of the point of intersection of the planes through A, B, C and parallel to the cooridnate planes is `(1)/(x^(2))+(1)/(y^(2))+(1)/(z^(2))=(1)/(ax)+(1)/(by)+(1)/(cz)`.

Text Solution

Verified by Experts

The correct Answer is:
`(x_(1),y_(1),z_(1))`
Promotional Banner

Topper's Solved these Questions

  • PLANES

    AAKASH SERIES|Exercise EXERCISE - 8.1 (VERY SHORT ANSWER QUESTIONS)|16 Videos

  • PLANES

    AAKASH SERIES|Exercise EXERCISE - 8.1 (SHORT ANSWER QUESTIONS)|16 Videos

  • PLANES

    AAKASH SERIES|Exercise SOLVED EXAMPLES|5 Videos

  • PERIODICITY EXTREME VALUES AND GRAPHS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|33 Videos

  • PROPERTIES OF TRIANGLES

    AAKASH SERIES|Exercise ADDITIONAL PRACTICE EXERCISE (LEVEL II) (Linked Comprehension Type Questions Passage -III:)|3 Videos

Similar Questions

Explore conceptually related problems

A variable plane passes through a fixed point (1,-2,3) and meets the coordinates axes at points A,B, C then the point of intersection of the planes thorugh A,B ,C parallel to the coordinates planes lies on

Find the equations of the planes passing through the line of intersection of the planes 3x-y+5z-6=0, x-2y+3z+7=0 and parallel to the coordinate planes.

Find the equation of the plane passing through the point (1,1,1) and parallel to the plane x+2y+3z-7=0

Find the equation of the plane passing through the point (1,2,-3) and parallel to the plane 2x-3y+6z=0

Find the cartesian equation of the plane through the point A (2,-1,-4) and parallel to the plane 4x-12y-3z-7=0 .

Equation of a line passing through (1,-2, 3) and parallel to the plane 2x+3y+z+5 = 0 is