Q19 of 76 Page 26

Find the equation of the set of all points whose distances from (0, 4) are of their distances from the line y = 9.

Given that we need to find the equation of set of all points whose distances from S(0,4) are of their distances from the line(M) y = 9.



Let P(x,y) be any point from the set of all points.


We know that distance between the points (x1,y1) and (x2,y2) is .


We know that the perpendicular distance from the point (x1,y1) to the line ax + by + c = 0 is .


⇒


⇒


⇒


⇒


⇒


⇒ 9x2 + 9y2 - 72y + 144 = 4y2 - 72y + 324


⇒ 9x2 + 5y2 = 180


∴ The equation of the ellipse is 9x2 + 5y2 = 180.


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