Find the equation of locus of p if the ratio of the distance from p to a (5,-4) and b (7,6) is 2:3
Answers
Given:
Two points A(5,-4) and B(7,6)
Distance of the two points from the point p is 2:3
To find:
The equation of the locus of P
Calculation:
Let the point be P(x,y).
The distance between the points A(5,-4) and P(x,y) is
d₁ = √(x-5)²+(y+4)²
The distance between the points B(7,6) and P(x,y) is
d₂ = √(x-7)²+(y-6)²
The ratio of their distances is 2:3
=> √(x-5)²+(y+4)² / √(x-7)²+(y-6)² = 2/3
(x-5)²+(y+4)² / (x-7)²+(y-6)² = 4/9
9[(x-5)²+(y+4)²] = 4[(x-7)²+(y-6)²]
9[ x²+25-10x+y²+16+8y] = 4[x²+49-14x+y²+36-12y]
9[x²+y²-10x+8y+41] = 4[x²+y²-14x-12y+85]
9x²+9y²-90x+72y+369 = 4x²+4y²-56x-48y+340
5x²+5y²-34x+120y+29 = 0
The equation of the locus of the point p is 5x²+5y²-34x+120y+29 = 0
Step-by-step explanation:
this sum is very easy understand
