Question

find an equation for the parabola that has its vertex at the origin and has its focus at the point: $(-5.26,0)$. enter your answer as an equation. note: answer should be exact. question help: video written example

Explanation:

Step1: Determine the form of the parabola equation

Since the vertex is at the origin \((0,0)\) and the focus is at \((-5.26,0)\) (on the \(x\) - axis), the parabola opens to the left. The standard form of a parabola that opens to the left with vertex \((h,k)=(0,0)\) is \(y^{2}=4p(x - h)\), where \((h + p,k)\) is the focus. Here, \(h = 0,k = 0\) and \(h + p=-5.26\), so \(p=-5.26\).

Step2: Substitute \(p\) into the standard form

Substitute \(p=-5.26\) into the equation \(y^{2}=4p(x)\). We get \(y^{2}=4\times(- 5.26)x\).

Answer:

\(y^{2}=-21.04x\)