Question

The equation of parabola which has the vertex at origin and axis is $ x- $ axis and also passes through the point $(4,3)$, is

• A. $ 9{{y}^{2}}=4x $
• B. $ 9{{y}^{2}}=-4x $
• C. $ 4{{y}^{2}}=-9x $
• D. $ 4{{y}^{2}}=9x $

Answer 1

Answer: (D)

Given, vertex is origin and axis is $ x- $ axis.
$ \therefore $ Equation of parabola is $ {{(y-0)}^{2}}=4a(x-0) $
$ \Rightarrow $ $ {{y}^{2}}=ax $
Since, it passes through the point (4,3)
$ \therefore $ $ {{(3)}^{2}}=4a.4 $
$ \Rightarrow $ $ a=\frac{9}{16} $
Thus, required equation is $ {{y}^{2}}=4.\frac{9}{16}x $
$ \Rightarrow $ $ 4{{y}^{2}}=9x $