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densk [106]
2 years ago
13

sketch the curve represented by the parametric equations (indicate the orientation of the curve), write the corresponding rectan

gular equation by eliminating the parameter.x=3t-5 y=5t+1

Mathematics
1 answer:
pychu [463]2 years ago
5 0

Answer:

Reduced equaton is 5x-3y+\frac{28}{3}=0.

Step-by-step explanation:

Given parametric equation is,

x=3t-5 and y=5t+1

Now, x=3t-5\implies t=\frac{x+5}{3} substitute in second equation we get,

y=\frac{5}{3}(x+5)+1

y=\frac{5}{3}x+\frac{28}{9}

\implies 5x-3y+\frac{28}{3}=0

which is the corresponding rectangular equation after eliinating the parameter.

Now consider,

y=\frac{5}{3}x+\frac{28}{9}

Of which,

Slope : \frac{5}{3}

when,

x=0, y=\frac{28}{9}=3.1

x=1, y=\frac{43}{9}=4.8; x=-1, y=\frac{13}{9}=1.4

x=2, y=\frac{58}{9}=6.4;  x=-2, y=\frac{-2}{9}=-0.2

x=3, y=\frac{73}{9}=8.1; x=-3, y=\frac{-17}{9}=-1.8

x=4, y=\frac{88}{9}=9.8; x=-4, y=\frac{-32}{9}=-3.6

x=5, y=\frac{103}{9}=11.4; x=-5, y=\frac{-47}{9}=-5.2

ans so on. Thus sketching th curve will look like given,

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