Question:
Let $y^{2}=8x$ be the equation of a parabola. Which one of the following is an arbitrary point on the parabola?
Let $y^{2}=8x$ be the equation of a parabola. Which one of the following is an arbitrary point on the parabola?
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Always identify the value of '$a$' first before writing the parametric coordinates.
Updated On: Apr 28, 2026
- $(2t, 4t^2)$
- $(2t^2, 4t^2)$
- $(2t^2, 2t^2)$
- $(2t, 2t^2)$
- $(2t^2, 4t)$
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The Correct Option is
Solution and Explanation
Step 1: Concept
For a parabola $y^2 = 4ax$, the parametric point is $(at^2, 2at)$.
Step 2: Analysis
Given $y^2 = 8x$, comparing with $y^2 = 4ax$ gives $4a = 8 \implies a = 2$.
Step 3: Calculation
Substitute $a = 2$ into $(at^2, 2at)$: $(2t^2, 2(2)t) = (2t^2, 4t)$. Final Answer: (E)
For a parabola $y^2 = 4ax$, the parametric point is $(at^2, 2at)$.
Step 2: Analysis
Given $y^2 = 8x$, comparing with $y^2 = 4ax$ gives $4a = 8 \implies a = 2$.
Step 3: Calculation
Substitute $a = 2$ into $(at^2, 2at)$: $(2t^2, 2(2)t) = (2t^2, 4t)$. Final Answer: (E)
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