Question

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

• A. $(2t^2+2,2t-3)$
• B. $(2t^2-2,2t-3)$
• C. $(2t^2-2,2t+3)$
• D. None of these

Answer 1

The correct option is B $(2t^2-2,2t-3)$

The equation of the parabola is ${(x+\frac{3}{2})}^2+{(y+3)}^2={\left(\frac{2x+5}{2}\right)}^2$

$\Rightarrow 4[x^2+\frac{9}{4}+3x]+4[y^2+9+6y]=(4x^2+25+20x)\Rightarrow (y^2+6y+9)-2(x+2)=0\Rightarrow {(y+3)}^2=2(x+2)$

Clearly, $x=2t^2-2$ and $y=2t-3$ satisfy it for all $t$.