The parametric point 3- t 2- 3 t -2 represents a parabola withA- focus at -3-2B- all of theseC- vertex at 3-2D- directrix x -5

The correct option is C vertex at (3, 2)We have, x = 3 + t^2 and y = 3t 2 nbsp; ⇒ x 3 = t^2 and y + 2 = 3t ⇒ (y + 2)^2 = 9 (x 3) which is a parabola ...

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Standard XII

Mathematics

Parametric Equation of Parabola

The parametri...

Question

The parametric point $(3 + t^{2}, 3 t - 2)$ represents a parabola with

focus at

(- 3, - 2)

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vertex at

(3, - 2)

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directrix

x = - 5

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all of these

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Solution

The correct option is B vertex at $(3, - 2)$
We have, $x = 3 + t^{2}$ and $y = 3 t - 2$
$\Rightarrow x - 3 = t^{2} and y + 2 = 3 t \Rightarrow (y + 2)^{2} = 9 (x - 3)$
which is a parabola with vertex at $(3, - 2)$ , focus at $(\frac{21}{4}, - 2)$ and directrix $x = \frac{3}{4}$

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The parametric point (3+t2,3t−2) represents a parabola with

The correct option is B vertex at (3,−2)We have, x=3+t2 and y=3t−2 ⇒x−3=t2 and y+2=3t⇒(y+2)2=9(x−3) which is a parabola with vertex at (3,−2), focus at (214,−2) and directrix x=34

The parametric point $(3 + t^{2}, 3 t - 2)$ represents a parabola with

The correct option is B vertex at $(3, - 2)$
We have, $x = 3 + t^{2}$ and $y = 3 t - 2$
$\Rightarrow x - 3 = t^{2} and y + 2 = 3 t \Rightarrow (y + 2)^{2} = 9 (x - 3)$
which is a parabola with vertex at $(3, - 2)$ , focus at $(\frac{21}{4}, - 2)$ and directrix $x = \frac{3}{4}$