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Chapter 6: Problem 32

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Horizontal axis and passes through the point (3,-2)

Short Answer

Expert verified
The standard form of the equation of parabola having vertex at origin and a horizontal axis passing through the point (3,-2) is \(y = -2/9x^2\).

Step by step solution

01

- Write down the basic form of equation

Since the parabola has a vertex at origin, the equation of the parabola is simplified to \(y = ax^2\).
02

- Substitute the given co-ordinates

Since the parabola passes through the point (3,-2), substitute these values into the equation, giving \(-2 = a(3)^2\).
03

- Solve for 'a'

Solving for 'a' in equation \(-2 = 9a\), we obtain \(a = -2/9\).
04

- Write the final equation

Substitute the value of a back into the equation \(y = ax^2\). Thus, the standard form of the parabola is \(y = -2/9x^2\).

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Most popular questions from this chapter

Identify the conic as a circle or an ellipse. Then find the center, radius, vertices, foci, and eccentricity of the conic (if applicable), and sketch its graph. \(\frac{(x-3)^{2}}{25 / 4}+\frac{(y-1)^{2}}{25 / 4}=1\)

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Find the standard form of the equation of the parabola with the given characteristics. Vertex: (1,2)\(;\) directrix: \(y=-1\)
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