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

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 $y^2=4.\frac{9}{16}x$
$\Rightarrow$ $4y^2=9x$