Question

Assertion :A homogeneous equation of second degree in $x,y,z$ represent a pair of planes through origin. Reason: A homogeneous equation of second degree in $x,y,z$ can be factorised into homogeneous linear factors.

• A. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion
• B. Both Assertion & Reason are individually true but Reason is not the ,correct (proper) explanation of Assertion
• C. Assertion is true but Reason is false
• D. Assertion is false but Reason is true

Answer 1

The correct option is A Both Assertion & Reason are individually true & Reason is correct explanation of Assertion

A homogeneous equation of second degree in $x,y,z$ represents a plane passing through origin.

Consider two planes $ax+by+cz=0,a_{1}x+b_{1}y+c_{1}z=0$

Their product is homogeneous.

$\therefore$ The homogeneous equation can be factorized into above two equations of planes.

Hence A is correct.