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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they do not intersect

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Solution

The correct option is A $4 x + 4 y + 4 z + 9 = 0$
$\begin{matrix} (x^{2} + y^{2} + z^{2} + 2 x + 2 y + 2 z + 2) - (x^{2} + y^{2} + z^{2} + x + y + z - \frac{1}{4}) = 0 x + y + z + \frac{1}{4} = 0 4 x + 4 y + 4 z + 9 = 0 H e n c e, o p t i o n A i s c o r r e c t a n s w e r . \end{matrix}$

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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

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

The equation of the circle which intersects circles $x^{2} + y^{2} + x + 2 y + 3 = 0, x^{2} + y^{2} + 2 x + 4 y + 5 = 0$ and

$x^{2} + y^{2} - 7 x - 8 y - 9 = 0$ at right angle, will be

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=0(x2+y2+z2+2x+2y+2z+2)−(x2+y2+z2+x+y+z−14)=0x+y+z+14=04x+4y+4z+9=0Hence,optionAiscorrectanswer.

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

The correct option is A $4 x + 4 y + 4 z + 9 = 0$
$\begin{matrix} (x^{2} + y^{2} + z^{2} + 2 x + 2 y + 2 z + 2) - (x^{2} + y^{2} + z^{2} + x + y + z - \frac{1}{4}) = 0 x + y + z + \frac{1}{4} = 0 4 x + 4 y + 4 z + 9 = 0 H e n c e, o p t i o n A i s c o r r e c t a n s w e r . \end{matrix}$