Question:
The equation of the parabola which is symmetric about the y-axis and passes through the point $(2, -3)$ is:
The equation of the parabola which is symmetric about the y-axis and passes through the point $(2, -3)$ is:
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For parabolas symmetric about the y-axis, always assume $x^2 = ky$ unless vertex shift is mentioned.
Updated On: Jun 16, 2026
- $4x^2 = -3y$
- $4x^2 = 3y$
- $3x^2 = 4y$
- $3x^2 = -4y$
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The Correct Option is D
Solution and Explanation
Concept:
A parabola symmetric about the y-axis has its axis along the y-axis and standard form:
\[
x^2 = ky
\]
where $k$ is a constant. The sign of $k$ determines whether the parabola opens upward or downward.
Step 1: Substitute the point into general form Given point: \[ (2, -3) \] Substitute into $x^2 = ky$: \[ (B)^2 = k(-3) \] \[ 4 = -3k \]
Step 2: Solve for constant $k$ \[ k = -\frac{4}{3} \] This negative value indicates that the parabola opens downward.
Step 3: Form the equation \[ x^2 = -\frac{4}{3}y \] Multiply throughout by 3 to remove fraction: \[ 3x^2 = -4y \]
Step 4: Geometrical interpretation Since $k < 0$, the parabola opens in the negative y-direction, which is consistent with the given point $(2,-3)$ lying below the x-axis. Final Answer: \[ \boxed{3x^2 = -4y} \]
Step 1: Substitute the point into general form Given point: \[ (2, -3) \] Substitute into $x^2 = ky$: \[ (B)^2 = k(-3) \] \[ 4 = -3k \]
Step 2: Solve for constant $k$ \[ k = -\frac{4}{3} \] This negative value indicates that the parabola opens downward.
Step 3: Form the equation \[ x^2 = -\frac{4}{3}y \] Multiply throughout by 3 to remove fraction: \[ 3x^2 = -4y \]
Step 4: Geometrical interpretation Since $k < 0$, the parabola opens in the negative y-direction, which is consistent with the given point $(2,-3)$ lying below the x-axis. Final Answer: \[ \boxed{3x^2 = -4y} \]
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