Question

A rod of fixed length 2 units moves so that it's ends are on the positive x-axis and that part of the line x+y=0 which lies in the second quadrant. Find the locus of the midpoint of rod. ANSWER ONLY IF YOU KNOW!!​

Answer 1

Answer:

the above is the answer

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Answer 2

Given : length of AB = 2 units

line= x+y=0

To find : Locus of the mid point of the rod

Explanation:

let the point on the x axis be (a,0)

on the line x+y = 0 be (-b,b) and let the mid point be (h,k)

coordinates of h = $\frac{a-b}{2}$

coordinates of k = $\frac{b}{2}$

length of AB = 2 units

therefore ,

(a+b) ² + b² = 4

(a-b)² +4ab +b²= 4

take a-b = 2h

b = 2k

a = 2k +2h

we get

(2h)² + 4(2k+2h) (2k)  + (2k)² = 4

h²+5k² +4hk-1=0

therefore

The locus of the mid point  is x²+5y²+4xy-1=0

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