Question

Equation of parabola having its focus at $S(2,0)$ and one extremes of its latus rectum as $(2,2)$ is

• A. $y^2=4(3-x)$
• B. $y^2=4(x-1)$
• C. both $\left(a\right)$ and $\left(b\right)$
• D. $noneofthese$

Answer 1

Answer: (C)

both $\left(a\right)$ and $\left(b\right)$

Distance Formula $=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

$\Rightarrow$$S(2,0)\equiv (x_1,y_1),(2,2)\equiv (x_2,y_2)$

Distance of semi latus rectum $=2a=$ $\sqrt{(2-2{)}^2+(2-0{)}^2}$

$\Rightarrow 2a=2$

$\therefore a=1$

$\therefore$ vertex can.$(2-1,0)$ or $(2+1,0)$

$\Rightarrow$$(1,0)$ , $(3,0)$

$\therefore y^2=4a(x-a)$

$\Rightarrow$$y^2=4(x-1)$ or $y^2=4(-1)(x-3)=4(3-x)$