Question

Given P.Q are two points an the curve y =log, (r-0.5) + log, v4x2 - 4x+1 Pis also lies on the circle
1
r+y=10.If Q lies inside the given circle such that its abscissae is integer then
Mar{Po
Equal to​

Answer 1

Step-by-step explanation:

Given P,Q are two points on the curve y = log1/2, (x- 0.5) + log2 v4x2 - 4x+1 and P lies on the circle x^2 + y^2 =10.If Q lies inside the given circle such that its abscissa is an integer then

• So y = log base ½  (x – 0.5) + log base 2 √4x^2 – 4x + 1
• Now log base a/b x = - log base b/a x
• So y = - log base2 (x – 0.5) + log base 2 √(2x – 1)^2
• So y = log base2 (2x – 1) – logbase2 (x – 0.5)
• So we have log a – log b = log a/b
• So y = log base 2 (2x – 1 / x – 0.5)
•        = log base2 2 (x – 0.5) / x – 0.5
•          = log 2 base 2
• So y = 1
• Now points of p (x1,1) and Q (x2,1)
• Now equation of circle is x^2 + y^2 = 10
•                         So x1^2 + 1 = 10
•                     Or x1^2 = 9
•                         Or x1 = 3
• Therefore the coordinates will be  p(3,1)

Reference link will be

https://brainly.in/question/7265174