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# need help on parametric equations watch

1. a) sketch the curve c whose parametric equations are
x= 2 cos t, y = 5 sin t, 0<t< pi

b) calculate the area of the finite region bounded by the curve c and the x axis.

c) find the equation of c in the form y=f(x)
2. x/2 = cos t y/5 = sin t

x²/4 = cos²t y²/25 = sin²t
x²/4 + y²/25 = 1
25x² + 4y² = 100

--------------

y = (sqrt(100-25x^2)) /2
y = 2.5sqrt(4-x²)
3. (Original post by Undry1)
x/2 = cos t y/5 = sin t

x²/4 = cos²t y²/25 = sin²t
x²/4 + y²/25 = 1
25x² + 4y² = 1

--------------

y = (sqrt(1-25x^2)) /2
is this for part B?
4. no that is the cartesian equation, he got it wrong on the second last line when he multiplied by 100.

the function looks like an ellipse, it crosses the x axis at 2, -2, crosses the y axis at 5 and -5.

integrate it to find the area.
5. the area of an ellipse is π*a*b where 2a and 2b are the lengths of the axes.

you are asked for half of this.

a = 2 and b = 5 so the area you require is π*2*5/2 = 5π
6. (Original post by the bear)
the area of an ellipse is π*a*b where 2a and 2b are the lengths of the axes.

you are asked for half of this.

a = 2 and b = 5 so the area you require is π*2*5/2 = 5π
my answer doesnt seem to be anything near this
7. i cant seem to be able to plot the graph on my graphic calculator, nothing seems to come up. anyone know what ive done wrong
8. are there any limits when intergrating?
9. Area = ∫5sint.-2sint.dt Limits: 0,π/2
= -∫10sin²t dt
=-∫10(½-½cos2t)dt
=-∫5-5cos2t dt
= -5t-2.5sint

Area = -(-5(π/2)-2.5sinπ/2)
Area = 2.5π+2.5

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