Question

Question 3- If any point is equidistant from the points (a+b, b-a) and (a-b, a+b), prove that bx = ay.​

Answer 1

Answer:

Let point P(x, y) is equidistant from A(a + b, b – a) and B(a – b, a + b), then AP = BP or AP2 = BP2 ((a + b) – x)2 + ((a – b) – y)2 = ((a – b) – x)2 + ((a + b) – y)2 (a + b)2 + x2 – 2(a + b)x + (a – b)2 + y2 – 2(a – b)y = (a – b)2 + x2 – 2(a – b)x + (a + b)2 + y2 – 2(a + b)y (a2 + b2 + 2ab + x2 – 2(a + b)x + b2 + a2 – 2ab + y2 – 2(a – b)y = (a2 + b2 – 2ab + x2 – 2(a – b)x + b2 + a2 + 2ab + y2 – 2(a + b)y => – 2(a + b)x – 2(a – b)y = – 2(a – b)x – 2(a + b)y => ax + bx + ay – by = ax – bx + ay + by => bx = ayRead more on Sarthaks.com - https://www.sarthaks.com/707511/if-the-point-x-y-is-equidistant-from-the-points-a-b-b-a-and-a-b-a-b-prove-that-bx-ay

Answer 2

Answer:

Step by step explanation is there.