Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

Equation of sphere passing through the points (2,0,0),(0,2,0),(0,0,2) and having least possible radius is

$(x^{2} + y^{2} + z^{2}) - 4 (x + y + z) - 3 = 0$
$3 (x^{2} + y^{2} + z^{2}) - 4 (x + y + z) - 4 = 0$
$4 (x^{2} + y^{2} + z^{2}) - 3 (x + y + z) - 5 = 0$
$(x^{2} + y^{2} + z^{2}) - (x + y + z) - 2 = 0$

hint Hint:

Let equation of the sphere be given by $x squared space plus space y squared space plus space z squared space plus space 2 u x space plus space 2 v y space plus space 2 w z space plus space d space equals space 0$
Find the value of d.

The correct answer is: $3 open parentheses x to the power of 2 end exponent plus y to the power of 2 end exponent plus z to the power of 2 end exponent close parentheses minus 4 left parenthesis x plus y plus z right parenthesis minus 4 equals 0$

Let equation of the sphere be given by $x squared space plus space y squared space plus space z squared space plus space 2 u x space plus space 2 v y space plus space 2 w z space plus space d space equals space 0$ ...... (1)
As the sphere passes through points (2, 0, 0), (0, 2, 0) and (0, 0, 2)
So, we have
2 + 4u + d = 0,
2 + 4v + d = 0 and
2 + 4w + d = 0
On solving,
u = v = w = $negative 1 fourth left parenthesis d space plus 2 right parenthesis$
If r is the radius of the sphere, then
$r space equals space √ left parenthesis u squared plus space v squared plus space w squared space minus space d right parenthesis rightwards double arrow r squared space equals space u squared plus space v squared plus space w squared space minus space d rightwards double arrow r squared space equals 3 over 4 space open parentheses d plus 2 close parentheses squared space minus space d space equals space m left parenthesis l e t right parenthesis F o r space v a l u e space space r space t o space b e space m i n i m u m fraction numerator d m over denominator d d end fraction space equals space 0 rightwards double arrow 3 over 4 space 2 open parentheses d plus 2 close parentheses space minus space 1 space equals space 0 rightwards double arrow space d space equals space minus 4 over 3$
Also,

$fraction numerator d squared m over denominator d d squared end fraction space equals space 3 over 2 space equals space p o s i t i v e space a t space d space equals space minus 4 over 3 H e n c e comma space m space i s space m i n i m u m space a t space d space equals space minus 4 over 3 S o comma space s u b s t i t u t i n g space v a l u e space o f space d comma space w e space h a v e space u space equals space v space equals space w space equals space minus 4 over 3 T h e r e f o r e space e q u a t i o n space o f space t h e space s p h e r e space space x squared space plus space y squared space plus space z squared space minus 4 over 3 left parenthesis x space plus space y space plus z space right parenthesis space minus space 4 over 3 space equals space 0$

Taking LCM
$3 open parentheses x to the power of 2 end exponent plus y to the power of 2 end exponent plus z to the power of 2 end exponent close parentheses minus 4 left parenthesis x plus y plus z right parenthesis minus 4 equals 0$
Thus, equation of sphere passing through the points (2,0,0),(0,2,0),(0,0,2) and having least possible radius is $3 open parentheses x to the power of 2 end exponent plus y to the power of 2 end exponent plus z to the power of 2 end exponent close parentheses minus 4 left parenthesis x plus y plus z right parenthesis minus 4 equals 0$

Related Questions to study

Identify $A$ to $D$ and choose the correct combination

Identify $A$ to $D$ and choose the correct combination

Choose the correct combination of labelling for the hormonal control of female reproductive system.

Choose the correct combination of labelling for the hormonal control of female reproductive system.

The RER in the cell synthesised protein which would be later used in building the plasma membrane. But it is observed that the protein in the membrane is slightly different from the protein made in the RER. The protein was probably modified in another cell organelle.
Identify the organelle in the given diagram.

The RER in the cell synthesised protein which would be later used in building the plasma membrane. But it is observed that the protein in the membrane is slightly different from the protein made in the RER. The protein was probably modified in another cell organelle.
Identify the organelle in the given diagram.

parallel

Go through the sectional view of a mitochondrion showing the different parts and identify the structures $A$ to $E$

Go through the sectional view of a mitochondrion showing the different parts and identify the structures $A$ to $E$

Which of the following is the correct representation of $A comma blank B$ and $C$ in the given figure of a chromosome?

Which of the following is the correct representation of $A comma blank B$ and $C$ in the given figure of a chromosome?

The following diagram shows some of the missing structures in a plant cell (A-E). Identify the structures

The following diagram shows some of the missing structures in a plant cell (A-E). Identify the structures

parallel

Correlate the given features of animal cells (I to VII) with their respective parts ( $A$ to $N$ )

I)The structure replicates during mitosis and generates the spindle
II)Major site for synthesis of lipid
III)Power house of the cell
IV)store house of digestive enzyme
V)Increase the surface are for the absorption of materials
VI)Site of glycolysis
VII)Site for active ribosomal RNA synthesis
The correct option is

Correlate the given features of animal cells (I to VII) with their respective parts ( $A$ to $N$ )

I)The structure replicates during mitosis and generates the spindle
II)Major site for synthesis of lipid
III)Power house of the cell
IV)store house of digestive enzyme
V)Increase the surface are for the absorption of materials
VI)Site of glycolysis
VII)Site for active ribosomal RNA synthesis
The correct option is

Identify $A$ to $D$ in the diagrammatic representation of internal structure of centrioles

Identify $A$ to $D$ in the diagrammatic representation of internal structure of centrioles

By eliminating $a comma b comma c$ from the Homogeneous Equations $x equals fraction numerator a over denominator b minus c end fraction comma y equals fraction numerator b over denominator c minus a end fraction comma z equals fraction numerator c over denominator a minus b end fraction$ where $a comma b comma c$ not all zero then $x y plus y z plus z x equals$

By eliminating $a comma b comma c$ from the Homogeneous Equations $x equals fraction numerator a over denominator b minus c end fraction comma y equals fraction numerator b over denominator c minus a end fraction comma z equals fraction numerator c over denominator a minus b end fraction$ where $a comma b comma c$ not all zero then $x y plus y z plus z x equals$

parallel

The electronic configuration of neon is

The electronic configuration of neon is

chemistry-General

The rank of $open square brackets table attributes columnalign right end attributes row 1 cell negative 1 end cell 1 1 row cell negative 1 end cell 1 1 2 row 1 1 cell negative 1 end cell 3 end table close square brackets$ is

The rank of $open square brackets table attributes columnalign right end attributes row 1 cell negative 1 end cell 1 1 row cell negative 1 end cell 1 1 2 row 1 1 cell negative 1 end cell 3 end table close square brackets$ is

The system of equations $alpha x plus y plus z equals alpha minus 1 comma x plus alpha y plus z equals alpha minus 1 comma x plus y plus alpha z equals alpha minus 1$ has no solution, if $alpha$ is

The system of equations $alpha x plus y plus z equals alpha minus 1 comma x plus alpha y plus z equals alpha minus 1 comma x plus y plus alpha z equals alpha minus 1$ has no solution, if $alpha$ is

parallel

The structure of the major product formed in the following reaction is

The structure of the major product formed in the following reaction is

chemistry-General

Identify the compound Y in the following reaction

Identify the compound Y in the following reaction