
If and are lying on and respectively then the range of is
A) [0, )
B) [0,1]
C) [0,17/2]
D) [0,3/2]
Answer
503.4k+ views
Hint: We know that the equation of circle with center A(a,0) and radius r is
We also know that the equation of ellipse with foci C(c,0) and D(d,0) and with length of major axis as a ‘l’ is
So the given equations are the equations of circle and ellipse. Draw a graph including both circle and ellipse and find the maximum and minimum distances.
Complete step by step answer:
If we draw the graph of given equations it will as the figure shown below.
By comparing the equation of the circle with the given equation we got to know that the center (A) is (3,0) and radius r is 4.
By comparing the equation of the ellipse with the given equation we got to know that the foci are C(-1,0) .
and D(1,0) and the length of the major axis FE is 3.
We know that CF=DE and CD=distance between (-1,0) and (1,0)=2
Length of major axis =FC+CD+DE=2FC+2
=>3=2FC+2
=>FC=1/2=DE
As FC and DE are 1/2,
F=(-3/2,0) ;
E=(3/2,0);
Now they have asked the value of where and are points on circle and ellipse respectively.
We know that distance is always a positive value. By looking at the graph we can easily say that if = = H or G then the value of will be Zero. So the minimum value of is 0.
Now coming to the maximum value, will be obviously F and from F we need to find maximum distance to the circle.
We know a property of a circle that the distance from an outside point to a circle will be maximum when the distance line passes through the centre, Which says the distance will be maximum when .
Therefore the maximum distance is FB= FC+CB= FC+2r=
Therefore the range will be [0,17/2].
The correct option is C.
Note:
In this problem all the numericals are almost integral values or easily solved, but not all the questions will be so. So, practice by taking other values and drawing graphs for those questions. In almost many problems you get the solutions by drawing graphs, so practice drawing graphs frequently.
We also know that the equation of ellipse with foci C(c,0) and D(d,0) and with length of major axis as a ‘l’ is
So the given equations are the equations of circle and ellipse. Draw a graph including both circle and ellipse and find the maximum and minimum distances.
Complete step by step answer:
If we draw the graph of given equations it will as the figure shown below.

By comparing the equation of the circle with the given equation we got to know that the center (A) is (3,0) and radius r is 4.
By comparing the equation of the ellipse with the given equation we got to know that the foci are C(-1,0) .
and D(1,0) and the length of the major axis FE is 3.
We know that CF=DE and CD=distance between (-1,0) and (1,0)=2
Length of major axis =FC+CD+DE=2FC+2
=>3=2FC+2
=>FC=1/2=DE
As FC and DE are 1/2,
F=(-3/2,0) ;
E=(3/2,0);
Now they have asked the value of
We know that distance is always a positive value. By looking at the graph we can easily say that if
Now coming to the maximum value,
We know a property of a circle that the distance from an outside point to a circle will be maximum when the distance line passes through the centre, Which says the distance will be maximum when
Therefore the maximum distance is FB= FC+CB= FC+2r=
Therefore the range will be [0,17/2].
The correct option is C.
Note:
In this problem all the numericals are almost integral values or easily solved, but not all the questions will be so. So, practice by taking other values and drawing graphs for those questions. In almost many problems you get the solutions by drawing graphs, so practice drawing graphs frequently.
Recently Updated Pages
Master Class 12 Business Studies: Engaging Questions & Answers for Success

Master Class 12 Economics: Engaging Questions & Answers for Success

Master Class 12 Maths: Engaging Questions & Answers for Success

Master Class 12 Biology: Engaging Questions & Answers for Success

Master Class 12 Physics: Engaging Questions & Answers for Success

Master Class 12 English: Engaging Questions & Answers for Success

Trending doubts
What is the Full Form of PVC, PET, HDPE, LDPE, PP and PS ?

Why should a magnesium ribbon be cleaned before burning class 12 chemistry CBSE

A renewable exhaustible natural resources is A Coal class 12 biology CBSE

Megasporangium is equivalent to a Embryo sac b Fruit class 12 biology CBSE

What is Zeises salt and ferrocene Explain with str class 12 chemistry CBSE

How to calculate power in series and parallel circ class 12 physics CBSE
