Chapter 8.2, Problem 27E

Solution

To find: Equation of parabola using focus and whose vertex is at $\left(0,0\right)$.

Hence, required equation of parabola is $y^2=-20x$.

Given: Focus of parabola is at $\left(-5,0\right)$ and vertex is at $\left(0,0\right)$.

Concept Used: Equation of parabola $y^2=4ax$ here focus is at $\left(a,0\right)$ and vertex is at $\left(0,0\right)$.

Calculation:

Focus of parabola is at $\left(-5,0\right)$ then value of $a=-5$

Substituting the value of $a=-5$ in standard form of parabola:

  $\begin{array}{l}{y}^2=4\times \left(-5\right)x\\ y^2=-20x\end{array}$

Conclusion:

Hence, required equation of parabola is $y^2=-20x$.