Doubt from area

Area bounded by parabola y²=4x with it’s latus rectum and Area bounded by parabola y²=-4x with it’s latus rectum will be same .
Just the region will be different graphically but area will be same in both of these cases

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Question no 19 i am confused about parabola what type of parabola it will form below x axis or above x axis

This is how the parabola and the required area will be formed

I think you found out wrong points equation of parabola would be (x+1)^2=-1(y-4) so according to this parabola will pass through (-1,4)

See carefully The parabola which is drew is passing through -1,4

Ok what about area i think i should subtract the equation of parabola from equation of line and apply limits from 0 to 1 ?

You’ll have to do that and in addition to it add the area between the line and the x axis from 1 to point of int of that line with x axis

But got wrong answer which is not matching with any options i got 41/42 sq units

There must be a calculation error
I am getting option A

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In question 2 second part i am getting 4a^2/3(root3+pi) instead of given in key please check

I am not satisfied with your working you put y function while integrating with respect to x

By mistake I have written dx instead of dy in 1 step.
I guess that was easily understandable

Rest all calculations are correct

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I hope , now it’s okay for you :relaxed:

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Suppose these are two given curves i want to find the area of common region please tell which region will be common

Are you sure that it’s about common area ? Because that will be :infinity:

If it’s about area bounded by these 2 curves then it should be

That will be a finite value

Which parabola should i substract from other to find area

For finding the area of bounded region or the common area?

I got it

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