CBSE Class 11-science Answered
Find the equation of the axis and the coordinates of the vertex of a parabola whose focus is the point(1,1) and whose directrix is the line 3x+4y-2=0.
Asked by bdroy_2014 | 10 Nov, 2018, 09:24: PM
Expert Answer
AS shown in figure, axis and directrix are perpendicular to each other.
Since directrix equation is 3x+4y-2 = 0, axis equation is of the form 4x-3y+k = 0, where k is a constant.
Since axis is passing through the focus S(1,1), we will substitute x=1, y=1 in axis equation and find constant k.
4x-3y+k = 4(1) - 3(1) +k = 0, hence k = -1 ;
Equation of axis is 4x-3y-1 = 0
Intersection point P of axis and directrix is obtained by solving both directrix and axis equations as shown below
3x+4y = 2 .....................(1)
4x-3y = 1 .....................(2)
By solving above simultaneous linear equations , we get x = 2/5, y = 1/5 ;
Hence coordinates of point of intersection P is (2/5 , 1/5)
vertex of parabola is mid-point of focus S and point P. hence vertex point is { [1+(2/5)]/2, [1+1/5)]/2 } = { 7/10, 6/10 }
Answered by Thiyagarajan K | 16 Nov, 2018, 12:16: AM
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