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Question
A ray of light moving parallel to the x-axis gets reflected from a parabolic mirror whose equation is (y−3)2=8(x+2). After reflection, the ray passes through the point (α,β) which lies on the axis of parabola, then what is the value of α+β+8?
A ray of light moving parallel to the x-axis gets reflected from a parabolic mirror whose equation is (y−3)2=8(x+2). After reflection, the ray passes through the point (α,β) which lies on the axis of parabola, then what is the value of α+β+8?
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Solution
The correct option is A 11
Upon reflection, all the rays of light parallel to the parabola’s axis pass through the parabola’s focus.
Thus,(α,β) is nothing but the focus of the parabola as (α,β) lies on the axis of parabola.
The equation of the given parabola is (y−3)2=8(x+2) having a=2.
This is a translated parabola having vertex (−2,3).
So, the coordinates of focus of translated parabola is given as (a+h,k) i.e (2−2,3)⇒(0,3).
On comparing we get α=0,β=3.
Hence, the value of α+β+8=0+3+8=11.
Upon reflection, all the rays of light parallel to the parabola’s axis pass through the parabola’s focus.
Thus,(α,β) is nothing but the focus of the parabola as (α,β) lies on the axis of parabola.
The equation of the given parabola is (y−3)2=8(x+2) having a=2.
This is a translated parabola having vertex (−2,3).
So, the coordinates of focus of translated parabola is given as (a+h,k) i.e (2−2,3)⇒(0,3).
On comparing we get α=0,β=3.
Hence, the value of α+β+8=0+3+8=11.
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