# How do you find the standard form of the equation of the parabola with a vertex of (1,0) and two points that are in the parabola are (5,3) and (5,-3)?

Aug 4, 2016

$4 {y}^{2} = 9 \left(x - 1\right)$.

#### Explanation:

As we look at the two given pts. $P \left(5 , 3\right) \mathmr{and} Q \left(5 , - 3\right)$ through which the reqd. Parabola passes, we immediately find that it is symmetric about X-axis.

So, its eqn. must be of the form $S : {y}^{2} = a x + b \ldots \ldots \ldots \ldots \left(1\right)$

The pts. $P , Q \mathmr{and} \left(1 , 0\right) a l l \in S$

$\therefore 9 = 5 a + b , 0 = a + b \Rightarrow 9 = 4 a \Rightarrow a = \frac{9}{4} , b = - \frac{9}{4}$

Hence, the Parabola $S : {y}^{2} = \frac{9}{4} \left(x - 1\right) , i . e . , 4 {y}^{2} = 9 \left(x - 1\right)$.