Question

Find the
parabola
the line
length of the
x = 3t^2, y =6t
3x-y-3=0
portion of the
cut off by​

Answer 1

Given : paramrtric equations are,

$x=3t^2\hfill (1)$

$y=6t\hfill (2)$

cut off by the line,

$3x-y-3$

To find : equation of parabola generated by (1)  and (2).    

Step-by-step explanation: so from (2) we get,

$y=6t\implies t=\frac{y}{6}$

substitute this in (1) we get,

$x=3t^2=3\times (\frac{y}{6})^2=3\times \frac{y^2}{36}=\frac{y^2}{12}$

$\therefore y^2=12x$

which is the requitred equation of parabola.

Answer 2

$y^2=12x$

Step-by-step explanation:

Given : Paramertric equations are,

$x=3t^2 ............. (i)$

$y=6t ........ (ii)$

cut off by the line,

$3x-y-3=0$

we have to find equation of parabola generated by (1)  and (2).    

so from (2) we get,

$y=6t\implies t=\frac{y}{6}$

substitute this in (1) we get,

$x=3t^2=3\times (\frac{y}{6})^2=3\times \frac{y^2}{36}=\frac{y^2}{12}$

$\therefore y^2=12x$

Hence  this is required equation of parabola.

To learn more

i)Find the length of the portion of the parabola x=3t^2, y=6t cut off by the line 3x+y-3=0

https://brainly.in/question/15814881

ii)If coordiante of pints A and B are on a number line are -3 and -7. to find d(A,B)​

https://brainly.in/question/8748660