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For the parabola y2 + 6 y − 2 x + 5 = 0
1. The vertex is − 2, − 3
2. The directrix is y + 3 = 0
Which of the following is correct?
1. The vertex is − 2, − 3
2. The directrix is y + 3 = 0
Which of the following is correct?
- a)Both 1 and 2 are true
- b)1 is true, 2 is false
- c)1 is false, 2 is true
- d)Both 1 and 2 are false
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
For the parabola y2 + 6 y − 2 x + 5 = 01. The vertex is − ...
Explanation:
Vertex of the parabola:
- The vertex of a parabola in the form y^2 + 6y - 2x + 5 = 0 can be found by completing the square for y.
- By completing the square, we get (y + 3)^2 - 9 - 2x + 5 = 0.
- Simplifying further, we get (y + 3)^2 = 2x + 4.
- Comparing this with the standard form (y - k)^2 = 4a(x - h), we find the vertex to be (-2, -3).
Directrix of the parabola:
- The equation of directrix for a parabola in the form y^2 = 4ax is y = -a.
- In this case, the directrix is at y = -3 (since a = 1/2).
- Therefore, the correct directrix equation should be y + 3 = 0.
Hence, the correct answer is option B - 1 is true, 2 is false.
Vertex of the parabola:
- The vertex of a parabola in the form y^2 + 6y - 2x + 5 = 0 can be found by completing the square for y.
- By completing the square, we get (y + 3)^2 - 9 - 2x + 5 = 0.
- Simplifying further, we get (y + 3)^2 = 2x + 4.
- Comparing this with the standard form (y - k)^2 = 4a(x - h), we find the vertex to be (-2, -3).
Directrix of the parabola:
- The equation of directrix for a parabola in the form y^2 = 4ax is y = -a.
- In this case, the directrix is at y = -3 (since a = 1/2).
- Therefore, the correct directrix equation should be y + 3 = 0.
Hence, the correct answer is option B - 1 is true, 2 is false.
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For the parabola y2 + 6 y − 2 x + 5 = 01. The vertex is − 2, − 32. The directrix is y + 3 = 0Which of the following is correct?a)Both 1 and 2 are trueb)1 is true, 2 is falsec)1 is false, 2 is trued)Both 1 and 2 are falseCorrect answer is option 'B'. Can you explain this answer?
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