Q. 305.0( 1 Vote )
Find the equation of the set of all points whose distance from (0, 4) are 
of their distance from the line y = 9.
Answer :
Let the point be P (x, y).
According to the question,
Distance of P from (x, y)
(Distance from the line y=9)
Distance between the (x,y)& (0,4) = 
[Distance Formula]
Perpendicular Distance (Between a point and line) = 
, whereas the point is 
and the line is expressed as ax + by + c = 0 i.e.., x(0) + y – 6 = 0 & point = (x,y)
Distance between y – 9 = 0 {x(0) +y – 9 = 0} & (x, y)
Squaring both the sides,
x2 + y2 - 8y + 16 
(y2 - 18y + 81)
9x2 + 9y2 - 72y + 144 = 4y2 - 72y + 324
9x2 + 5y2 = 180
Hence, the required equation is 9x2 + 5y2 = 180
, which is an ellipse.
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