IIT JEE , AIEEE Forum - Mathematics , Algebra

sreeee

Hi please

1. find the area included between the curves y^2 = 4ax and x^2 + y^2 = 8x
which lies above the x axis.

please do not solve just tell which area should we take

draw figure and u will see that two areas are there above x axis . but which area?

akhil_o

edit*

see shaded area

thats the only area INCLUDED between the two curves,
the other one is inside circle but outside the parabola

ramkumar_november

akhil_o........ your figure is wrong.......

the circle has center (4,0) and radius 4........

so the circle and parabola must meet at the origin............

sboosy

It is a very nice point u ask there.This question is very much there in CBSE NCERT text but i think the solution there is wrong .

See the area enclosed between the curves (Parabola and Circle) is asked.

so according to definition ,(Parts of the curves should form the boundary of the area u r going to consider). Here x axis (the way in which the question is worded is not one of the curves).It is just said "area above x axis".So actually u shud consider the small area (almost convex shaped) between the curves,and not the bigger area above x axis.(bcos if u take this then it means u r considering x axis also as one of the curves which is wrong).

I think the answer so obtained is 4pi - 32/3

sboosy

Akhil ..u hav said "That s the area included between the 2 curves"
Now as far as i can see there are 3 curves.
parabola,circle and the x axis
which u have missed
so the other area is actually the required area

akhil_o

i am sorry dude i didnt get u...

forget the x-axis for now,,,
draw the figure BETWEEN the two curves, ie
included in both curves
since outer area u mention is OUTSIDE the parabola,
i did not consider it
now plug in the above-x-axis,
and eliminate the loweer half of the shaded area

plz corrrect me

ramkumar_november

yes sboosy , the answer is 4pi - (32/3) ........

the figure given by akhil is correct but the shaded region is wrong.......

the required area must be the area of smaller region between the circle and the parabola (only above the x-axis)........

akhil_o

plese explain why!

ramkumar_november

wait read the question properly :::::::::

" find the area included between the curves y^2 = 4ax and x^2 + y^2 = 8x
which lies above the x axis. "

the area which you have shaded in your post is

that is the larger region is

" area included between y²=4ax and x²+ y²= 8x and x-axis "

the area which i have mentioned is the smaller region.......

"area included between y²=4ax and x²+ y²= 8x (only) ......... and lying above the x-axis......."

understood????

for reference :

this sum is in RD SHARMA page number 21.37 problem 48 ........

the answer is 4pi - 32/3 .....

akhil_o

so do we always just find smaller areas unless mentioned?

sreeee

yup friends

i also did what sboosy is saying

But i dont think that cbse is going to give us the marks for that.

not even 1 mark as our figure is wrong which is supposed to carry 1 mark but only if it is correct.(as per cbse it is wrong though!)

sreeee

i also gt the answer as

4pi - 32/3

but they will be checking it according to ncert textbook

:(

ramkumar_november

you should read the question very carefully..... and then you should decide whether it is the smaller area or the larger area.........

if it is already mentioned in the question (like " find the smaller area between the circle and the parabola " )there is no problem..........

layman

No nothing is mentioned. But I had the same doubt too.

Ask & Discuss Questions with Community & Experts