Let a circle $C:x^2+y^2=1$ and two parabolas $P_1:y^2=4(x-1)$ and $P_2:y^2=-4(x+1)$
Both parabolas slides on the circle towards each other with same angular velocity such that they are tangent to circle and their axis are normal to circle after $9$ minutes
They get coincident first time, then:
If $P_1$ and $P_2$ intersect each other during their rotation then their point of intersection lies on $(x\neq 0)$
A) $4x^2+y^4+8y^2=0$
B) $4x^2+y^4+4y^2=0$
C) $8x^2+y^4+8y^2=0$
D) $8x^2+y^4+4y^2=0$
In this I could not get a good start .
And by seeing the options, I thought how this can be possible as in LHS everything is positive and it is equated to zero
Blue parabolas in the diagram are $P_1$ and $P_2$. They touch red lines $y=\pm x$ at points $(\pm2,\pm2)$.
After a $45°$ rotation, they will arrive at the position of the green parabolas in the diagram, line $x=0$ touching both at $(0,2\sqrt2)$.