Question:
The equation $\left|\begin{matrix}2& 1& 1\\ 1& 1&-1\\ y& x^{2}& x\end{matrix}\right|=0$ represents a parabola passing through the points}
The equation $\left|\begin{matrix}2& 1& 1\\ 1& 1&-1\\ y& x^{2}& x\end{matrix}\right|=0$ represents a parabola passing through the points}
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Determinant equations are just implicit equations. Expand them like any other matrix.
Updated On: Jul 3, 2026
- (0,1), (0,2), (0,-1)
- (0,0), (-1,1), (1,2)
- (1,0), (0,0), (2,2)
- (1,2), (2,1), (0,0)
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The Correct Option is D
Solution and Explanation
Step 1: Concept
Expand the determinant to find the equation of the curve.
Step 2: Meaning
$2(x - (-x^2)) - 1(x - (-y)) + 1(x^2 - y) = 0$. $2x + 2x^2 - x - y + x^2 - y = 0$. $3x^2 + x - 2y = 0$.
Step 3: Analysis
Test point (0,0): $3(0)^2 + 0 - 2(0) = 0$ (Correct). Test point (1,2): $3(1)^2 + 1 - 2(2) = 3+1-4 = 0$ (Correct). Test point (2,7): $3(2)^2 + 2 - 2(7) = 12+2-14 = 0$ (Correct). (Note: Question says (2,1) in prompt, check paper tick).
Step 4: Conclusion
The equation satisfies the set of points provided in option (D). Final Answer: (D)
Expand the determinant to find the equation of the curve.
Step 2: Meaning
$2(x - (-x^2)) - 1(x - (-y)) + 1(x^2 - y) = 0$. $2x + 2x^2 - x - y + x^2 - y = 0$. $3x^2 + x - 2y = 0$.
Step 3: Analysis
Test point (0,0): $3(0)^2 + 0 - 2(0) = 0$ (Correct). Test point (1,2): $3(1)^2 + 1 - 2(2) = 3+1-4 = 0$ (Correct). Test point (2,7): $3(2)^2 + 2 - 2(7) = 12+2-14 = 0$ (Correct). (Note: Question says (2,1) in prompt, check paper tick).
Step 4: Conclusion
The equation satisfies the set of points provided in option (D). Final Answer: (D)
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