AMU Engineering 2018 solved paper Solved Paper

Given a ray of light passing through the points (1,2) reflects on the X -axis at point A(x,0) and the reflected rays passes through (5,3) Slope of line PA
i.e. tan(90+θ)=

−2

x−1

⇒cot‌θ=

2

x−1

........(i)
Again slope of line QA
i.e., tan(90−θ)=

−3

x−5

cot‌θ=frac‌−3‌x−5 ........(ii)
From Eqs. (i) and (ii), we get

2

x−1

=

−3

x−5

⇒2x−10=−3x+3
⇒5x=13
⇒x=13∕5
∴ Coordinates of A is (

13

5

,0).