Question

# If sum of distances of a point from the origin and lines x=2 is 4, then its locus is

A
x212y=36
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B
y2+12x=36
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C
y212x=36
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D
x2+12y=36
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Solution

## The correct option is B y2+12x=36Solution:- (B) y2+12x=36Let the point be (h,k).Distance of the point (h,k) from the origin (0,0)-d1=√(h−0)2+(k−0)2=√h2+k2Distance of the point (h,k) from the line x−2=0-d2=h−2√12=h−2Given that the sum of distance of the point (h,k) from the origin and the line x=2 is 4.∴√h2+k2+(h−2)=4⇒√h2+k2=4−h+2⇒√h2+k2=6−hSquaring both sides, we have(√h2+k2)2=(6−h)2⇒h2+k2=36+h2−12h⇒k2+12h=36Replacing h with x and k with y, we havey2+12x=36Hence the locus of the point is y2+12x=36.

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