If the equal sides A B and A C (each equal to 5 units) of a right-angled isosceles triangle A B C are produced to P and Q such that B P . C Q = A B 2 , then the line P Q always passes through the fixed point (where A is the origin and A B , A C lie along the positive x and positive y -axis respectively)

Question

If the equal sides A B and A C (each equal to 5 units) of a right-angled isosceles triangle A B C are produced to P and Q such that B P . C Q = A B 2 , then the line P Q always passes through the fixed point (where A is the origin and A B , A C lie along the positive x and positive y -axis respectively), 7,6, 6,5, 5,5, 6,6

MARKS App · Accepted Answer

Let, A P = h , A Q = k Equation of the line P Q is x h + y k = 1 … 1 Given, B P . C Q = A B 2 ⇒ h - 5 k - 5 = 25 or, 5 h + 5 k = h k or, 5 h + 5 k = 1 From 2 , it follows that line 1 , i.e., P Q passes through the fixed point 5,5

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