Question

Observe the following Lists:

List-l	List - II
A. Length of the latusrectum of the parabola $3y^2=-4x$	1. $(5,2)$
B.Equation of the parabola whose focus $($0,4 $)$ and directrix $x+4=0$ is	2. $\frac{-4}{3}$
C. The focus of the parabola $(y-2{)}^2=8(x-3)$ is	3. $\frac{4}{3}$
D. Equation of the parabola whose vertex $(-1,-2)$ latusrectum 4 and axis is parallel to y-axis	4. $(x+1{)}^2=4(y+2)$
	5. $x^2=16y$

• A. $A-3,B-5,C-1,D-4$
• B. $A-3,B-5,C-4,D-1$
• C. $A-3,B-2,C-1,D-4$
• D. $A-1,B-2,C-3,D-4$
  

Answer 1

The correct option is A $A-3,B-5,C-1,D-4$

A) Length of latusrectum is given by $4a$ and here $4a$ = $\frac{4}{3}$

B) Here focus is at $(0,4)$ so $a=4$ and directrix is given by $x+4$ so the equation of parabola is $x^2=16y$

C) Focus is given by $(a+h,o+k)$ were $(h,k)$ is the enter of hyperbola so here $a=2$ and center of hyperbola is at $(3,2)$ so focus is $(5,2)$

D) Equation of parabola is ${(x+1)}^2=4(y+2)$