Coordinates of parametric point on the parabola- whose focus is -3-2-3 and the directrix is 2 x -5-0 is given by A- 2 t2-2-2 t-3B- 1-2 t 2-2- t -3C- 1-2 t2-2- t-3D- 1-2 t2-2- t-3

The correct option is B (12t^2 2, t 3)(x + 32 )^2 + (y + 3)^2 = (2x+ 52 )^2 ⇒ 4 [x^2 + 94 + 3x ]+ 4 [y^2 + 9 + 6y] = (4x^2 + 25 + 20x) ⇒ (y^2 + 6y + 9) ...

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Standard XII

Mathematics

Parametric Equation of Parabola

Coordinates o...

Question

Coordinates of parametric point on the parabola, whose focus is $(\frac{- 3}{2}, - 3)$ and the directrix is $2 x + 5 = 0$ is given by

(2 t^{2} + 2, 2 t - 3)

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(\frac{1}{2} t^{2} - 2, t - 3)

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(\frac{1}{2} t^{2} - 2, t + 3)

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(\frac{1}{2} t^{2} + 2, t + 3)

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Solution

The correct option is B $(\frac{1}{2} t^{2} - 2, t - 3)$
${(x + \frac{3}{2})}^{2} + (y + 3)^{2} = {(\frac{2 x + 5}{2})}^{2} \Rightarrow 4 [x^{2} + \frac{9}{4} + 3 x] + 4 [y^{2} + 9 + 6 y] = (4 x^{2} + 25 + 20 x) \Rightarrow (y^{2} + 6 y + 9) - 2 (x + 2) = 0$
or $(y + 3)^{2} = 2 (x + 2)$
Here $a = \frac{1}{2}$
Therefore $x = \frac{1}{2} t^{2} - 2$ and $y = t - 3$ satisfy it for all $t$ .

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Parametric Equation of Parabola

Standard XII Mathematics

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Coordinates of parametric point on the parabola, whose focus is (−32,−3) and the directrix is 2x+5=0 is given by

The correct option is B (12t2−2,t−3)(x+32)2+(y+3)2=(2x+52)2⇒4[x2+94+3x]+4[y2+9+6y]=(4x2+25+20x)⇒(y2+6y+9)−2(x+2)=0 or (y+3)2=2(x+2) Here a=12 Therefore x=12t2−2 and y=t−3 satisfy it for all t.

Coordinates of parametric point on the parabola, whose focus is $(\frac{- 3}{2}, - 3)$ and the directrix is $2 x + 5 = 0$ is given by