The relation between x and y such that the distance of the
point (x,y) from the point (2, 3) is twice of its distance
from the point (1,5), is
A 3x2 + 3y2 - 4x - 34y + 91 = 0
B
3x2 + 4y2 + 12x + 40y + 109 - 0
с
2x2 + 3y2 + 11x + 36y - 119 = 0
D
3x2 + 2y2 + 4x + 44y - 109 = 0
Answers
Answered by
22
Answer :-
Option - a
Topic :-
Co - ordinate Geometry
Given :-
The point (x, y) is from the point (2, 3) is twice the distance from point (1, 5)
To find:-
- The relation between x and y
Solution :-
Let ,
- P =(x, y)
- A = (2, 3)
- B = (1 , 5 )
According to the question ,
Distance between P and A is twice the distance between P and B So,
PA = 2 PB
By using distance formula
Squaring on both sides
Simplifying the equation :-
Expanding the equation by algebraic identity (a-b)²= a²-2ab+b²
Transposing R.H.S equation to L.H.S
Take common -
Hence option "a" is the correct
Used formulae:-
- Distance formula
( a- b)² = a²- 2ab + b²- Algebraic identity
Answered by
28
TO FIND -:
- Find the equation of the locus of the point whose distance from y-axis is half the distance from origin .
S O L U T I O N :
- Let us assume that , such a point R exists with the coordinates
( h, k ) .
- Now , the distance of the point from the y axis is half the distance from the origin .
Coordinates of that point on the Y axis -
Here ,
Replacing the coordinates by x and y -
_________________________________________
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