Question

Find the equation of the parabola with vertex at the origin, the axis along the X-axis and passing through the point P(3, 4)
1. \( \rm y^2=\frac{4}{3}x\)
2. \( \rm y^2=\frac{3}{16}x\)
3. \( \rm y^2=-\frac{9}{16}x\)
4. \( \rm y^2=\frac{16}{3}x\)

Answer 1

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.