Question

The vertex of a parabola is the point $(a,b)$ and latus rectum is of the length $l.$ If the parabola is upward opening and its axis is parallel to the $y-$axis, then its equation is

• A. $(x+a{)}^2=l(y-b)$
• B. $(x-a{)}^2=l(y-b)$
• C. $(x+a{)}^2=\frac{l}{2}(y-b)$
• D. $(x-a{)}^2=\frac{l}{4}(y-b)$

Answer 1

The correct option is B $(x-a{)}^2=l(y-b)$

Parabola having axis parallel to $y-$axis is
$(x-a{)}^2=4A(y-b)$.
According to question, length of latus rectum $4A=l$.
Hence, equation of parabola is
$(x-a{)}^2=4\times \frac{l}{4}(y-b)$
or $(x-a{)}^2=l(y-b)$