Question

find the equation of pa​

Answer 1

Answer:

Step-by-step explanation:

We have,

The equation of a parabola whose vertex is at the origin and its axis is parallel to the x-axis will be of the form

$\tt{y^2=4\,a\,x\,\,\,\,\,or\,\,\,\,\,y^2=-4\,a\,x}$

Since the parabola is passing through (1, - 3), so, it will be a right-handed parabola and its equation will be of the form    y² = 4ax  

Now, it is passing through (1, - 3)

$\sf{y^2=4\,a\,x}$

$\sf{\implies\,(-3)^2=4\,a(1)}$

$\sf{\implies\,9=4\,a}$

$\sf{\implies\,a=\dfrac{9}{4}}$

So, the required equation of the parabola is

$\tt{y^2=4\cdot\dfrac{9}{4}\cdot\,x}\\\\\tt{\implies\,y^2=9\,x}$