The maximum number of common normals of $y^2=4ax$ and $x^2=4by$ is equal to

Suppose $BOAC$ is a rectangle in the $XY$-plane where $O$ is the origin and $A, B$ lie on the parabola $y=x^2$. Then,$C$ must lie on the curve

Let $P(x, y)$ be the midpoint of the line joining $(1, 0)$ to a point on the curve $y^{2} = \left|\begin{array}{ll}x+1 & x+2 \\ x+3 & x+5\end{array}\right|$. Then,the locus of $P$ is symmetrical about

Find the equation of the parabola with vertex $(-3, 0)$ and directrix $x + 5 = 0$.

If the points of intersection of the parabolas $y^2=5x$ and $x^2=5y$ lie on the line $L$,then the area of the triangle formed by the directrix of one parabola,the latus rectum of another parabola,and the line $L$ is

Let $L$ be a normal to the parabola $y^2=4x$. If $L$ passes through the point $(9,6)$,then $L$ is given by
$(A)$ $y-x+3=0$ $(B)$ $y+3x-33=0$ $(C)$ $y+x-15=0$ $(D)$ $y-2x+12=0$