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IPMAT Indore 2024 - QA (MCQ) Q26 Explanation
November 25, 2024
Explanation:
(b) let ∠𝐴𝑃𝐵 = 𝜃
Equation of circle given is 𝑥2 + 𝑦2 − 14𝑥 + 16𝑦 + 88 = 0
∴ Centre coordinates (7,−8)
And radius = √g^2 +f^2 −c = √(7−0)^2 +(8)^2-88 = √25 = 5
PO = √(7−0)2 +(−8−7/2 )^2 = = √49+(−23/2)^2 = √49 + 529/4 = √725/4
Applying Pythagoras theorem, in ∆PAO, we get
PA^2 +AO^2 = PO^2
PA^2 = PO^2−AO^2
PA =√PO^2−AO^2 = √725/4-25 = 25
In △ PAO, tan(θ/2) = AO/PA = 5/(25/2) = 2/5
∴ tan2θ = 2tan (θ/2)/1-tan^2(θ/2) = = 2⋅(2/5)/1−4/25 = (1/5)/(2/2) = 20/21 Ans.