The plane of intersection of $x^{2} + y^{2} + z^{2} + 2 x + 2 y + 2 z + 2 = 0$ and $4 x^{2} + 4 y^{2} + 4 z^{2} + 4 x + 4 y + 4 z - 1 = 0$

4 x + 4 y + 4 z - 9 = 0

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x + y + z + 9 = 0

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4 x + 4 y + 4 z + 1 = 0

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x + y + z + 1 = 0

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Solution

The correct option is A $4 x + 4 y + 4 z - 9 = 0$
Assume $S_{1} : x^{2} + y^{2} + z^{2} + 2 x + 2 y + 2 z + 2 = 0$ and $S_{2} : 4 x^{2} + 4 y^{2} + 4 z^{2} + 4 x + 4 y + 4 z - 1 = 0$
Therefore plane of intersection is given by,
$S_{2} - 4 S_{1} = 0$
$\Rightarrow (4 x^{2} + 4 y^{2} + 4 z^{2} + 4 x + 4 y + 4 z - 1) - 4 (x^{2} + y^{2} + z^{2} + 2 x + 2 y + 2 z + 2) = 0$
$\Rightarrow 4 x + 4 y + 4 z - 9 = 0$

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Similar questions

Q. The plane of intersection of

x^{2} + y^{2} + z^{2} + 2 x + 2 y + 2 z + 2 = 0

and

4 x^{2} + 4 y^{2} + 4 z^{2} + 4 x + 4 y + 4 z - 1 = 0

Q. The plane of intersection of

x^{2} + y^{2} + z^{2} + 2 x + 2 y + 2 z + 2 = 0

and

4 x^{2} + 4 y^{2} + 4 z^{2} + 4 x + 4 y + 4 z - 1 = 0

is:

Q. The point at which the axes are translated to remove first degree terms is

List - I	List - II
$A) x^{2} + y^{2} + z^{2} - 2 x$ $- 4 y + 2_{Z} - 3 = 0$	1. $(- 1, - 2, 1)$
$B) x^{2} + y^{2} - z^{2} + 2 x$ $+ 4 y + 2_{Z} + 3 = 0$	2. $($ 1, 2, 1 $)$
$C) 2 x^{2} - 2 y^{2} + z^{2} - 4 x$ $+ 8 y - 2_{Z} - 5 = 0$	$3. (- 1, 1, 2)$
$D) 2 x^{2} - 3 y^{2} + z^{2} + 4 x$ $+ 6 y - 4_{Z} - 2 = 0$	$4. (1, 2, - 1)$

Q. Centre of the sphere

4 (x - 7) (x + 2) + 4 (y - 4) (y + 9) +

4 (z + 1) (z - 1) + 175 = 0

Find the equation of circle which touches $2 x - y + 3 = 0$ and pass through the points of intersection of the line $x + 2 y - 1 = 0$ and the circle $x^{2} + y^{2} - 2 x + 1 = 0$

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The plane of intersection of x2+y2+z2+2x+2y+2z+2=0 and 4x2+4y2+4z2+4x+4y+4z−1=0

The correct option is A 4x+4y+4z−9=0Assume S1:x2+y2+z2+2x+2y+2z+2=0 and S2:4x2+4y2+4z2+4x+4y+4z−1=0Therefore plane of intersection is given by,S2−4S1=0 ⇒(4x2+4y2+4z2+4x+4y+4z−1)−4(x2+y2+z2+2x+2y+2z+2)=0⇒4x+4y+4z−9=0

The plane of intersection of $x^{2} + y^{2} + z^{2} + 2 x + 2 y + 2 z + 2 = 0$ and $4 x^{2} + 4 y^{2} + 4 z^{2} + 4 x + 4 y + 4 z - 1 = 0$