Find the equation of the parabola with vertex at the origin, passing throgh the point P(3,-4) and symmetric about the y-axis.

Explanation

It is given that the vertex of the parabola is O(0,0) and it is symmetric about the y-axis, So, its equation is `x^(2)=4ay or x^(2)=-4ay`. Since the parabola passes through the point `P(3,-4)` so it lies in the 4th quadrant.
`therefore` it is downward parabola. Let the equation be `x^(2)=-4ay`. Since it passes through the point P(3,-4) we have `3^(2)=-4xx a xx(-4) Rightarrow a=(9)/(16)`
So, the required equation is
`x^(2)=-4xx(9)/(16)y Rightarrow x^(2)=(-9)/(4)y Rightarrow 4x^(2)+9y=0`