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The shortest distance (in units) between the parabolas y2 = 4x and y2=2x−6 is
- a)2
- b)√5
- c)3
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The shortest distance (in units) between the parabolas y2 = 4x andy2=2...
We can find the distance between the parabolas by finding the distance between their closest points.
First, let's rewrite the equations in terms of y:
y = ±√(4x)
y = ±√(2x)
To find the closest points, we need to set the two equations equal to each other:
±√(4x) = ±√(2x)
Squaring both sides, we get:
4x = 2x
x = 0
Plugging x = 0 into either equation, we get the y-coordinate of the closest point:
y = ±√(0) = 0
Therefore, the closest points are (0,0) on both parabolas.
To find the distance between these points, we can use the distance formula:
d = √[(x2 - x1)2 + (y2 - y1)2]
d = √[(0 - 0)2 + (0 - 0)2]
d = √(0)
d = 0
Therefore, the shortest distance between the parabolas is 0 units.
First, let's rewrite the equations in terms of y:
y = ±√(4x)
y = ±√(2x)
To find the closest points, we need to set the two equations equal to each other:
±√(4x) = ±√(2x)
Squaring both sides, we get:
4x = 2x
x = 0
Plugging x = 0 into either equation, we get the y-coordinate of the closest point:
y = ±√(0) = 0
Therefore, the closest points are (0,0) on both parabolas.
To find the distance between these points, we can use the distance formula:
d = √[(x2 - x1)2 + (y2 - y1)2]
d = √[(0 - 0)2 + (0 - 0)2]
d = √(0)
d = 0
Therefore, the shortest distance between the parabolas is 0 units.
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Community Answer
The shortest distance (in units) between the parabolas y2 = 4x andy2=2...
Shortest distance between two curves occurs along the common normal.
Normal to y2=4x at (m2, 2m) is
y+mx−2m−m3=0
Both normals are same, if −2m−m3=−4m−
⇒m=0, ±2
So, points will be (4, 4) and (5, 2) or (4,−4) and (5,−2)
Hence, shortest distance will be
Normal to y2=4x at (m2, 2m) is
y+mx−2m−m3=0
Both normals are same, if −2m−m3=−4m−
⇒m=0, ±2
So, points will be (4, 4) and (5, 2) or (4,−4) and (5,−2)
Hence, shortest distance will be
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