MHTCET 2016 Math Solved Paper

(a) It is given that, the foot of perpendicular from point Q(a, b, c) to the yz plane is A(0, b, c) and tire foot of perpendicular from point Q to the zx plane is B(a, 0, c).
Let the equation of plane passing through the point (0,0,0) be Ax + By + Cz = 0 .....(i)
As it is passing through the point A(0, b, c) and B( a,0,c).
So, 0 +Bb + Cc = 0 and Aa + 0 + Cc = 0
⇒ Cc = Bb and Cc = -Aa
Therefore, -Aa = -Bb = Cc = k
⇒ A=−

k

a

,B=−

k

b

and C=

k

c

−

k

a

x−

k

b

y+

k

c

z=0[ From Eq.(i)]
⇒ −

x

a

−

y

b

+

z

c

=0 or

x

a

+

y

b

−

z

c

=0