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If (h, k) is a point on the axis of parabola 2(x -1)2 + 2 (y -1)2 = (x + y + 2)2 from where three distinct normals can be drawn, then
- a)h > 2
- b)h < 4
- c)h > 8
- d)h < 8
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If (h, k) is a point on the axis of parabola 2(x -1)2 + 2 (y -1)2 = (x...
which is of the following PM2 = SP2∴ Focus= (1,1) . Directrix is x+y+2 =0
Axis is x-y=0 and z= (-1,-1)
Vertex = (0,0). Parameter a = √2
The distance of the point from vertex and lie on axis from which 3 normals can be drawn must be greater 2a = 2√2. Hence point on axis at a distance 2√2 is (2,2), Hence h>2
Most Upvoted Answer
If (h, k) is a point on the axis of parabola 2(x -1)2 + 2 (y -1)2 = (x...
The given equation of the parabola is 2(x - 1)^2 + 2(y - 1)^2 = (x + y + 2)^2.
To find the points on the axis of the parabola, we set y = 0 and solve for x:
2(x - 1)^2 + 2(0 - 1)^2 = (x + 0 + 2)^2
2(x - 1)^2 + 2 = (x + 2)^2
2(x^2 - 2x + 1) + 2 = x^2 + 4x + 4
2x^2 - 4x + 2 + 2 = x^2 + 4x + 4
x^2 - 8x + 4 = 0
Using the quadratic formula, we have:
x = (-(-8) ± √((-8)^2 - 4(1)(4))) / (2(1))
x = (8 ± √(64 - 16)) / 2
x = (8 ± √48) / 2
x = (8 ± 4√3) / 2
x = 4 ± 2√3
So, the points on the axis of the parabola are (4 + 2√3, 0) and (4 - 2√3, 0).
To find the value of h, we take the average of the x-coordinates of these points:
h = (4 + 2√3 + 4 - 2√3) / 2
h = 8 / 2
h = 4
Therefore, h = 4.
To find the points on the axis of the parabola, we set y = 0 and solve for x:
2(x - 1)^2 + 2(0 - 1)^2 = (x + 0 + 2)^2
2(x - 1)^2 + 2 = (x + 2)^2
2(x^2 - 2x + 1) + 2 = x^2 + 4x + 4
2x^2 - 4x + 2 + 2 = x^2 + 4x + 4
x^2 - 8x + 4 = 0
Using the quadratic formula, we have:
x = (-(-8) ± √((-8)^2 - 4(1)(4))) / (2(1))
x = (8 ± √(64 - 16)) / 2
x = (8 ± √48) / 2
x = (8 ± 4√3) / 2
x = 4 ± 2√3
So, the points on the axis of the parabola are (4 + 2√3, 0) and (4 - 2√3, 0).
To find the value of h, we take the average of the x-coordinates of these points:
h = (4 + 2√3 + 4 - 2√3) / 2
h = 8 / 2
h = 4
Therefore, h = 4.
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If (h, k) is a point on the axis of parabola 2(x -1)2 + 2 (y -1)2 = (x + y + 2)2 fromwhere three distinct normals can be drawn, thena)h > 2b)h < 4c)h > 8d)h < 8Correct answer is option 'A'. Can you explain this answer?
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