The Student Room Group

C4 parametric equations

1f7275f75c85caf7a3546e31eafd276f.png

Part (a) I got y2=36x24x4 y^2 = 36x^2 - 4x^4
Part (b) I got A = 27
Part (c) I got 18

For part (d) how would I find the height of the rectangle to work out it's area?
Do I differentiate y=2x(9x2)1/2 y = 2x (9-x^2)^{1/2} and find the stationary point?
Reply 1
Original post by IgorYakov
1f7275f75c85caf7a3546e31eafd276f.png

Part (a) I got y2=36x24x4 y^2 = 36x^2 - 4x^4
Part (b) I got A = 27
Part (c) I got 18

For part (d) how would I find the height of the rectangle to work out it's area?
Do I differentiate y=2x(9x2)1/2 y = 2x (9-x^2)^{1/2} and find the stationary point?


Since the sides are tangents to the curve, you only need to find the maximum value of y = 9sin2t and from there, you can find the height of the rectangle.
Reply 2
Original post by Blazy
Since the sides are tangents to the curve, you only need to find the maximum value of y = 9sin2t and from there, you can find the height of the rectangle.




Why would I not need to convert it in to Cartesian form then do it? Just so I understand fully
Reply 3
Original post by mastermdc
Are you sure that A = +27. Hint: What is the derivative of cos(x) Double check the sign.



But as the limits were the 'wrong' way round so you put a minus at the front right?
Reply 4
Original post by IgorYakov
Why would I not need to convert it in to Cartesian form then do it? Just so I understand fully


It's easier to see the maximum of x and y just by looking and cos and sin, rather than playing about with y^2 = f(x) (plus, it's only 4 marks and you've done the majority of the work in the previous parts, assuming they're all right of course).

You can do it the way you suggested in the first post (though I suggest leaving it as what you got in part a and then doing an implicit differentiation on it rather than take square roots).
Reply 5
Original post by IgorYakov
But as the limits were the 'wrong' way round so you put a minus at the front right?


Right. The equation x=3costx=3\cos t gives us that x=3x = 3 when t=0t=0 and that x=0x=0 when t=π2t=\frac{\pi}{2}. So the appropriate integrals are:

A=x=0x=3ydx=t=π/2t=027sin2tsintdt=t=0t=π/227sin2tsintdtA = \int_{x=0}^{x=3} y dx = \int_{t=\pi/2}^{t=0} -27 \sin 2t \sin t dt = \int^{t=\pi/2}_{t=0} 27 \sin 2t \sin t dt
Reply 6
Original post by atsruser
Right. The equation x=3costx=3\cos t gives us that x=3x = 3 when t=0t=0 and that x=0x=0 when t=π2t=\frac{\pi}{2}. So the appropriate integrals are:

A=x=0x=3ydx=t=π/2t=027sin2tsintdt=t=0t=π/227sin2tsintdtA = \int_{x=0}^{x=3} y dx = \int_{t=\pi/2}^{t=0} -27 \sin 2t \sin t dt = \int^{t=\pi/2}_{t=0} 27 \sin 2t \sin t dt



Yeah that's what I did made it positive as I've flipped the integral limits
Reply 7
I have worked out the answer to the part d and I am getting 36cm^2. Could you please tell me if I am right or wrong? Thank You.


Posted from TSR Mobile
Reply 8
you dont need to find stationary point to find the height of the rectangle. to find the y coordinate look at the equation y=9sin2t you know that the highest sin can be is 1 therefore highest y can be is y=9*1, y=9 the lowest y can be is -9 as sin cant be lower than -1 this gives you a height if 18. now for the x coordinate the highest cos can be is 1 thus highest value of x is 3 and lowest is -3 this gives you a width of 9 the area of the rectangle is therefore 18*9=162. I cant remember what i got for the area of the blue shape however you will just get your answer for c and multiple it by 4 then take it away from 162.

i hope that is correct xD
Reply 9
Thank you for the reply ma'am. For me, total area for the blue glass came out to be 18*4= 72cm^2
As for the width of the ABCD rectangle, wouldn't it be 6 in total and not 9? Thus giving me (9+9)*6= 108cm^2 for the total area of the ABCD rectangle. So to get the area of the red glass, it would have been simply 108-72 leading to 36cm^2.

I could show you my working out if it will be of any help to you in order to see where I have went wrong, that is IF if I am wrong which is likely to be the case. But 36cm^2 is what I get.

Thank You for your help.
(edited 9 years ago)
Reply 10
Oops yeah it is 6 I cant think what answer I got but I will get my homework back either tomorrow or Tuesday so I can confirm then but your answer does sound right. I just wantrd to share the quicker way of finding area of rectangle with you :smile:
Thank You ma'am for your reply. I greatly appreciate your help and concern. Please do guide me once you have received your feedback for your homework. Thank you again.


Posted from TSR Mobile
Original post by IgorYakov
1f7275f75c85caf7a3546e31eafd276f.png

Part (a) I got y2=36x24x4 y^2 = 36x^2 - 4x^4
Part (b) I got A = 27
Part (c) I got 18

For part (d) how would I find the height of the rectangle to work out it's area?
Do I differentiate y=2x(9x2)1/2 y = 2x (9-x^2)^{1/2} and find the stationary point?


Where is this question from/
Reply 13
Original post by Ilovemaths96
Where is this question from/


From my textbook - Elmwood - Pure mathematics C3 and C4

I just searched the question online and found it so pasted that here instead of trying to draw it out

Quick Reply