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# Write the functions on parameter form?

a) (x^2)/4 + (y^2)/9 = 1

b) 4(x^2) + 9(y^2) = 36

c) (x-1)^2 + (y+2)^2 = 9

### 1 Answer

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- Steve4PhysicsLv 76 months ago
Remember sin²(t) + cos²(t) = 1.

________

a)

x²/4 + y²/9 = 1

(x/2)² + (y/3)² = 1

Since sin²(t) + cos²(t) = 1

Let sin(t) = x/2

Let cos(t) = y/3

x = 2sin(t) a nd y = 3cos(t)

________

b)

4x² + 9y² = 36

We want '1' on the right hand side so divide equation by 36.

x²/9 + y²/4 = 1

then use the same method as for a).

________

c)

(x-1)² + (y+2)² = 9

((x-1)/3)² + ((y+2)/3)² = 1

sin(t) = (x-1)/3

x = 2sin(t) + 1

You can find the equation for y the same way

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