Question

Answer the following problem using the figure,

If a > 0 the equation of the parabola is of the form:

$$\begin{gathered} a){\left(y-k\right)}^2=4a\left(x-h\right) \\ b){\left(y-k\right)}^2=-4a\left(x-h\right) \\ c){\left(x-h\right)}^2=4a\left(y-k\right) \\ d){\left(x-h\right)}^2=-4a\left(y-k\right) \end{gathered}$$

Short answer

The correct option is option (c).

Step-by-step solution

Step 1. Given information.

We have given equations of the parabola is,

$$\begin{gathered} a){\left(y-k\right)}^2=4a\left(x-h\right) \\ b){\left(y-k\right)}^2=-4a\left(x-h\right) \\ c){\left(x-h\right)}^2=4a\left(y-k\right) \\ d){\left(x-h\right)}^2=-4a\left(y-k\right) \end{gathered}$$

We have given graph is,

Step 2. Concept used.

The general equation of the parabola is,

${\left(y-k\right)}^2=4a\left(x-h\right)and{\left(x-h\right)}^2=4a\left(y-k\right)$

Step 3. Explanation.

We have given graph is the graph of upward parabola.

Hence, equation of the given parabola is,

${\left(x-h\right)}^2=4a\left(y-k\right)$.

Step 4. Conclusion.

Hence, If $a>0$ then equation of the parabola is ${\left(x-h\right)}^2=4a\left(y-k\right)$.