Three Dimensional Geometry

Section: Mathematics

Question : 48 of 58

Marks: +1, -0

The distance from a point (1,1,1) to a variable plane π is 12 units and the points of intersections of the plane π and X,Y,Z-axes are A,B,C respectively. If the point of intersection of the planes through the points A,B,C and parallel to the coordinate planes is P, then the equation of the locus of P is

[AP EAPCET 20 May 2024 Shift 1]

(‌
1
xy
+‌
1
yz
+‌
1
zx
)=143(‌
1
x2
+‌
1
y2
+‌
1
z2
)
‌
1
x2
+‌
1
y2
+‌
1
z2
=144
(‌
1
x
+‌
1
y
+‌
1
z
−1)2=144(‌
1
x2
+‌
1
y2
+‌
1
z2
)
(‌
1
x
+‌
1
y
+‌
1
z
−1)2=144(‌
1
x2
+‌
1
y2
+‌
1
z2
)2

Validate

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