Home
Class 12
MATHS
The locus of P(x,y) such that sqrt(x^2+...

The locus of `P(x,y)` such that `sqrt(x^2+y^2+8y+16)-sqrt(x^2+y^2-6x+9)=5,` is

A

hyperbola

B

circle

C

finite line segment

D

infinite ray

Text Solution

Verified by Experts

The correct Answer is:
D
We have `sqrt(x^(2)+(y+4)^(2)) -sqrt((x-3)^(2)-y^(2))=5`. The distance between the two points (3,0) and `(0,-4)` is 5.

Locus of P is the part of line `(x)/(3) -(y)/(4) =1`.
Promotional Banner

Similar Questions

Explore conceptually related problems

x dy - y dx = sqrt(x^(2) + y^(2)) dx

If the locus of the moving poin P(x,y) satisfying sqrt((x-1)^(2)+y^(2))+sqrt((x+1)^(2)+(y-sqrt(12))^(2))=a is an ellipse, then find the values of a.

The solution of (x dx+y dy)/(x dy-y dx)=sqrt((1-x^2-y^2)/(x^2+y^2)) is

A common tangent to 9x^2-16y^2 = 144 and x^2 + y^2 = 9 , is

If y=(x+sqrt(x^2+a^2))^n ,t h e n(dy)/(dx) is (a) (n y)/(sqrt(x^2+a^2)) (b) -(n y)/(sqrt(x^2+a^2)) (c) (n x)/(sqrt(x^2+a^2)) (d) -(n x)/(sqrt(x^2+a^2))

A variable chord of the circle x^2+y^2=4 is drawn from the point P(3,5) meeting the circle at the point A and Bdot A point Q is taken on the chord such that 2P Q=P A+P B . The locus of Q is (a) x^2+y^2+3x+4y=0 (b) x^2+y^2=36 (c) x^2+y^2=16 (d) x^2+y^2-3x-5y=0

Find the locus of a point which moves so that the ratio of the lengths of the tangents to the circles x^2+y^2+4x+3=0 and x^2+y^2-6x+5=0 is 2: 3.

The locus of a point that is equidistant from the lines x+y - 2sqrt2 = 0 and x + y - sqrt2 = 0 is (a) x+y-5sqrt2=0 (b) x+y-3sqrt2=0 (c) 2x+2y-3 sqrt2=0 (d) 2x+2y-5sqrt5=0

Show that f (x,y) = (2x ^(2) -y ^(2))/sqrt(x ^(2) + y ^(2)) is a homogeneous function of degree 1.

The equation sqrt((x+4)^2+(y+2)^2)+sqrt((x-4)^2+(y-2)^2)=8 represents a