JEE MATHEMATICS MCQ: 3D GEOMETRY SYSTEM

1 Easy

1 of 1

Application +4 | -1

A variable line through the point

\left( {\frac{1}{5},\frac{1}{5}} \right)

cuts the coordinate axes in the points

A

and

B

. If the point

P

divides

AB

internally in the ratio 3:1, then the locus of

P

View answer and explanation

Correct option: B

y + 3x = 20xy

Option B (

y + 3x = 20xy

) is correct because by finding the equation of a line passing through (1/5, 1/5) and using the section formula to express the coordinates of point P in terms of the intercepts, the locus of P can be derived as

y + 3x = 20xy

More Questions from 3D GEOMETRY SYSTEM

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The mid point of the line joining the points

\left( { - 10,\;8} \right)

and

\left( { - 6,\;12} \right)

divides the line joining the points

\left( {4,\; - 2} \right)

and

\left( { - 2,\;4} \right)

in the ratio The equation of the plane perpendicular to the

y z

-plane and passing through the points

(1,-2,4)

and

(3,-4

5)

is The value of

p

for which the lines

2 x+y-3=0

3 x-y-2=0

and

x-p y+5=0

may intersect at a point is If the vertices of a triangle at

O\left( {0,0} \right),A\left( {a,0} \right)

and

B\left( {0,a} \right).

Then, the distance between its circumcentre and orthocentre is The coordinates of the foot of the perpendicular drawn from the point

A(1,0,3)

to the join of the points

B(4,7,1)

and

C(3,5,3)

are The area of the triangle formed by the three lines

\frac{x}{1}=\frac{y}{2}=\frac{z}{3}, \frac{x}{2}=\frac{y}{1}=\frac{z}{3}

and

\frac{x-1}{1}=\frac{2-y}{2}, z=3