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Question
The equation 3x2+10xy+11y2+14x+12y+5=0 represents
🎥 Video solution / Text Solution of this question is given below:
Rule for Classifying Conics Using Discriminant
Given the equation: Ax2+Bxy+Cy2+Dx+Ey+F=0
Compute: Δ=B2−4AC
? Based on value of Δ:
- Ellipse: Δ<0 and A≠C, B≠0 → tilted ellipse
- Circle: Δ<0 and A=C, B=0
- Parabola: Δ=0
- Hyperbola: Δ>0
Example:
For the equation: 3x2+10xy+11y2+14x+12y+5=0
A=3, B=10, C=11 →
Δ=102−4(3)(11)=100−132=−32
Since Δ<0, it represents an ellipse.
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