Chapter 11, Problem 50RE

To determine

To Find: The equation of the parabola with given vertex $v\left(-1,0\right)$

Answer to Problem 50RE

The equation of the parabola is

  $y^2=4\left(x+1\right)$

Explanation of Solution

Given information:

Vertex $(-1,0)$ and touches y axis at $2$ i.e. $\left(0,2\right)$

Calculation:

Equation of parabola with vertex $\left(h,k\right)$ and axis parallel to x − axis is given as

  ${\left(y-k\right)}^2=4a\left(k-h\right)$ where $a=$ distance from focus and vertex.

Equation of parabola with vertex $v\left(-1,0\right)$ is

  $\begin{array}{l}{\left(y-k\right)}^2=4a\left(k-h\right)\\ y^2=4a\left(x+1\right)\end{array}$

It is also given that, this touches y − axis at $2$ i.e. $\left(0,2\right)$

  $\begin{array}{l}{\left(2\right)}^2=4a\left(0+1\right)\\ 4=4a\left(1\right)\\ a=1\end{array}$

Hence, The Equation of require parabola is $y^2=4\left(1\right)\left(x+1\right)$

  $y^2=4\left(x+1\right)$