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Question
Find foci of the equation $x^2 + 2x – 4y^2 + 8y – 7 = 0$
🎥 Video solution / Text Solution of this question is given below:
Finding Foci of a Conic
Given Equation: \( x^2 + 2x - 4y^2 + 8y - 7 = 0 \)
Step 1: Complete the square
⇒ \( (x + 1)^2 - 4(y - 1)^2 = 4 \)
Rewriting: \( \frac{(x + 1)^2}{4} - \frac{(y - 1)^2}{1} = 1 \)
This is a horizontal hyperbola with:
- Center: \( (-1, 1) \)
- \( a^2 = 4 \), \( b^2 = 1 \)
- \( c = \sqrt{a^2 + b^2} = \sqrt{5} \)
✅ Foci: \( (-1 \pm \sqrt{5},\ 1) \)
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