KEAM 2015 Math Paper

Equation of plane passes through line of intersection of the plane
2x−8y+4z=p and
3x−5y+4z+10=0 is
Given equation of plane is
x+3y+13=0....(ii)
Eqs. (i) and (ii) represent same plane.
∴4+4λ=0⇒λ=−1
Putting λ=−1 in Eq. (i), we get
−x−3y−p−10=0
⇒‌‌x+3y+p+10=0....(iii)
Comparing the coefficient of x,y and z constants term for Eqs. (i) and (ii), we get
p+10=13
⇒‌‌p=3