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The mirror image of the directrix of the parabola y2=4(x+1) in the line mirror x+2y=3, is
- a)x=−2
- b)4y−3x=16
- c)x−3y=0
- d)x+y=0
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The mirror image of the directrix of the parabolay2=4(x+1)in the line ...
-1
b)x=1
c)x=2
d)x=3
Solution:
The directrix of the parabola y2=4ax is given by the equation y=-a. So, the directrix of the given parabola y2=4(x-1) is y=-1.
The line of mirror x+2y=3 can be written as x=3-2y. We need to find the mirror image of the directrix y=-1 in this line.
The mirror image of a point (x,y) in the line x+2y=3 is given by the point (3-2y,x). So, the mirror image of the point (0,-1) (which lies on the directrix) is (3-2(-1),0), which simplifies to (5,0).
Therefore, the mirror image of the directrix y=-1 in the line mirror x+2y=3 is x=5 (since it is parallel to the y-axis).
Answer: x=5
b)x=1
c)x=2
d)x=3
Solution:
The directrix of the parabola y2=4ax is given by the equation y=-a. So, the directrix of the given parabola y2=4(x-1) is y=-1.
The line of mirror x+2y=3 can be written as x=3-2y. We need to find the mirror image of the directrix y=-1 in this line.
The mirror image of a point (x,y) in the line x+2y=3 is given by the point (3-2y,x). So, the mirror image of the point (0,-1) (which lies on the directrix) is (3-2(-1),0), which simplifies to (5,0).
Therefore, the mirror image of the directrix y=-1 in the line mirror x+2y=3 is x=5 (since it is parallel to the y-axis).
Answer: x=5
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Community Answer
The mirror image of the directrix of the parabolay2=4(x+1)in the line ...
for the given parabola , y2=4(x+1)
directrix is x=−2. and Any point on it is (−2, k)
let mirror image of (-2,k) in the line x+2y=3 is (x,y)
From Eqs. (i) and (ii), we get
⇒4y -3x = 16 is the equation of the mirror image of the directrix.
directrix is x=−2. and Any point on it is (−2, k)
let mirror image of (-2,k) in the line x+2y=3 is (x,y)
From Eqs. (i) and (ii), we get
⇒4y -3x = 16 is the equation of the mirror image of the directrix.
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The mirror image of the directrix of the parabolay2=4(x+1)in the line mirror x+2y=3,isa)x=−2b)4y−3x=16c)x−3y=0d)x+y=0Correct answer is option 'B'. Can you explain this answer?
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