Find the equation of set of all points sum of whose distance from (3,0) and(9,0 )is constant and equal to 12

Asked by deepakagarwal1024 | 24th Dec, 2018, 09:03: AM

Expert Answer:

Let P(x, y) bethe point on the given locus. Also, A(3, 0) and B(9, 0)
According to the question,
PA + PB = 12
begin mathsize 16px style square root of open parentheses straight x minus 3 close parentheses squared plus straight y squared end root space plus space square root of open parentheses straight x minus 9 close parentheses squared plus straight y squared end root equals 12 end style
begin mathsize 16px style square root of open parentheses straight x minus 3 close parentheses squared plus straight y squared end root equals 12 minus square root of open parentheses straight x minus 9 close parentheses squared plus straight y squared end root
end style
Squaring on both sides and solving we get
x - 18 = -2begin mathsize 16px style square root of open parentheses straight x minus 9 close parentheses squared plus straight y squared end root end style
Squaring on both sides and solving we get
3x2 + 4y2 - 36x = 0 which is ellipse

Answered by Sneha shidid | 24th Dec, 2018, 09:42: AM

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