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The equation of the tangent at the vertex of the parabola x2 + 4x + 2y = 0 is
- a)x = –2
- b)x = 2
- c)y = 2
- d)y = –2.
Correct answer is option 'C'. Can you explain this answer?
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The equation of the tangent at the vertex of the parabola x2+ 4x + 2y ...
-2
To find the equation of the tangent at the vertex of the parabola, we need to first find the coordinates of the vertex. We can do this by completing the square:
x^2 + 4x + 2y = 0
x^2 + 4x + 4 + 2y = 4
(x + 2)^2 = -2y + 4
So the vertex is at (-2, 2).
Next, we need to find the slope of the tangent at the vertex. We can do this by taking the derivative of the equation of the parabola:
2x + 4 + 0 = 0
2x = -4
x = -2
So the slope of the tangent at the vertex is 2(-2) + 4 = 0.
Finally, we can use the point-slope form of a line to find the equation of the tangent:
y - 2 = 0(x + 2)
y - 2 = 0
y = 2
So the equation of the tangent at the vertex is y = 2.
To find the equation of the tangent at the vertex of the parabola, we need to first find the coordinates of the vertex. We can do this by completing the square:
x^2 + 4x + 2y = 0
x^2 + 4x + 4 + 2y = 4
(x + 2)^2 = -2y + 4
So the vertex is at (-2, 2).
Next, we need to find the slope of the tangent at the vertex. We can do this by taking the derivative of the equation of the parabola:
2x + 4 + 0 = 0
2x = -4
x = -2
So the slope of the tangent at the vertex is 2(-2) + 4 = 0.
Finally, we can use the point-slope form of a line to find the equation of the tangent:
y - 2 = 0(x + 2)
y - 2 = 0
y = 2
So the equation of the tangent at the vertex is y = 2.
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The equation of the tangent at the vertex of the parabola x2+ 4x + 2y = 0 isa)x = –2b)x = 2c)y = 2d)y = –2.Correct answer is option 'C'. Can you explain this answer?
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