What is the focus of the parabola y= – x2? Simplify any fractions.

Identify 'a' value: We are given the equation of the parabola: y = –x^2. To find the focus, we need to identify the value of 'a' in the standard form of a parabola y = ax^2. Here, a = –1.Standard form of parabola: The standard form of a parabola with its vertex at the origin (0,0) and axis of symmetry along the y-axis is y = ax^2. The focus of such a parabola is given by the point (0, 1/(4a)).Substitute 'a' value: Substitute a = –1 into the formula for the focus (0, 1/(4a)). Focus of the parabola: (0, 1/(4 * (–1))).Calculate focus: Calculate the value of 1/(4 * (–1)). Focus of the parabola: (0, –1/4).

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What is the focus of the parabola $y= -x^2$ ? $\newline$ Simplify any fractions.

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Find the focus or directrix of a parabola

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Q. What is the focus of the parabola

y= -x^2

\newline

Simplify any fractions.

Identify 'a' value: We are given the equation of the parabola: $y = -x^2$ . To find the focus, we need to identify the value of 'a' in the standard form of a parabola $y = ax^2$ . Here, $a = -1$ .
Standard form of parabola: The standard form of a parabola with its vertex at the origin $(0,0)$ and axis of symmetry along the y-axis is $y = ax^2$ . The focus of such a parabola is given by the point $(0, \frac{1}{4a})$ .
Substitute 'a' value: Substitute $a = -1$ into the formula for the focus $(0, \frac{1}{4a})$ . $\newline$ Focus of the parabola: $(0, \frac{1}{4 \times (-1)})$ .
Calculate focus: Calculate the value of $\frac{1}{4 \times (–1)}$ . $\newline$ Focus of the parabola: $(0, –\frac{1}{4})$ .