Parabola
Consider the curve traced by the parametric pair x = 2t^2 and y = 4t as the parameter t varies over all real numbers; identify the Cartesian equation.
Select the correct option:
🔒 Solution Hidden from View
Submit your answer to unlock the detailed step-by-step solution.
More coordinate geometry Practice Questions
For the parabola described by y^2 = 12x, determine the coordinates of its focus together with the eq...
For the parabola described by y^2 = 12x, determine the coordinates of its focus together with the eq...
A chord of the parabola y^2 = 8x passes through its focus and is perpendicular to the axis; what is ...
A chord of the parabola y^2 = 8x passes through its focus and is perpendicular to the axis; what is ...
The standard equation of a parabola with vertex at origin and focus on positive x-axis is
The standard equation of a parabola with vertex at origin and focus on positive x-axis is
The focus of the parabola y² = 8x is
The focus of the parabola y² = 8x is
Statement: the lines 2x - 3y + 5 = 0 and 3x + 2y - 7 = 0 are mutually perpendicular; which option co...
Statement: the lines 2x - 3y + 5 = 0 and 3x + 2y - 7 = 0 are mutually perpendicular; which option co...
A point divides the line segment joining (2, -3) and (8, 9) internally in the ratio 1 : 2; what are ...
A point divides the line segment joining (2, -3) and (8, 9) internally in the ratio 1 : 2; what are ...
A point moves so that the sum of squares of its distances from the two points (3, 0) and (-3, 0) sta...
A point moves so that the sum of squares of its distances from the two points (3, 0) and (-3, 0) sta...
A rectangular hyperbola is described by the equation xy = 8 in the coordinate plane; what is the val...
A rectangular hyperbola is described by the equation xy = 8 in the coordinate plane; what is the val...
An ellipse has foci separated by a distance of 6 units and a sum of focal radii equal to 10 for ever...
An ellipse has foci separated by a distance of 6 units and a sum of focal radii equal to 10 for ever...
The straight line 4x + 3y - 24 = 0 forms a triangle with the two coordinate axes; what is the area o...
The straight line 4x + 3y - 24 = 0 forms a triangle with the two coordinate axes; what is the area o...
From the external point (5, 1) a tangent is drawn to the circle x^2 + y^2 = 9; what is the length of...
From the external point (5, 1) a tangent is drawn to the circle x^2 + y^2 = 9; what is the length of...
A moving point keeps its distance from the point (4, 0) always equal to its distance from the vertic...
A moving point keeps its distance from the point (4, 0) always equal to its distance from the vertic...
About This Question
- Subject
- mathematics
- Chapter
- coordinate geometry
- Topic
- parabola
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
y2=8x
Eliminating the parameter from a parametric pair recovers the Cartesian relation, and recognizing the resulting form lets us classify the conic. From y = 4t we get t = y/4, and substituting into x = 2t^2 gives x = 2(y/4)^2 = 2 · y^2/16 = y^2/8. Multiplying through, y^2 = 8x, a right-opening parabola. Option y^2 = 4x would arise from x = t^2 rather than 2t^2. Option x^2 = 8y wrongly treats x as the squared parameter expression. Option y^2 = 16x comes from mis-squaring y = 4t as if x = t^2. This is the standard JEE Advanced parametric-to-Cartesian elimination, a recurring conic technique. Plausibility check: comparing y^2 = 8x with y^2 = 4ax gives a = 2, and sample t = 1 yields the point (2, 4), which satisfies 16 = 8·2, confirming the curve passes through the generated points consistently.
This medium difficulty mathematics question is from the chapter coordinate geometry, covering the topic of parabola. It appeared in the 2025 exam.
Looking for more practice? Explore all mathematics questions or browse coordinate geometry questions on RankGuru.