Correct Answer - Option 4 :
\( \rm y^2=\frac{16}{3}x\)
Concept:
Equation of parabola having vertex at origin and along X-axis: y2 = 4ax
Calculation:
It is given that the vertex of the parabola is at the origin and its axis lies along the X-axis. So,its equation is \(\rm y^2=4ax\) OR \(\rm y^2=-4ax\)
Since it passes through the point P(3, 4), so it lies in the first quadrant.
∴ Its equation is \(\rm y^2=4ax\)
Now, P(3, 4) lies on it, so
\(\rm 4^2=4a(3)=12a\)
\(\rm \Rightarrow a = \frac43\)
∴ The required equation is \(\rm y^2=4(\frac43)x\)
\(\Rightarrow \rm y^2=\frac{16}{3}x\)
Hence, option (4) is correct.