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QJEEM24Ma27ae: JEE Main 2024 Mathematics - Class 11 JEEM24Ma27ae Solution: Equations of two diameters of a circle are and . The line…

Equations of two diameters of a circle are 2x−3y=52 x-3 y=5 and 3x−4y=73 x-4 y=7 . The line joining the points (−227,−4)\left(-\frac{22}{7},-4\right) and (−17,3)\left(-\frac{1}{7}, 3\right) intersects the circle at only one point P(α,β)P(\alpha, \beta) . Then, 17β−α17 \beta-\alpha is equal to _________.

Step-by-Step Verified Solution

Centre of circle is (1,−1)(1,-1)

JEE Main 2024 (Online) 29th January Morning Shift Mathematics - Circle Question 20 English Explanation

Equation of ABA B is 7x−3y+10=0…7 x-3 y+10=0 \ldots (i)

Equation of CP\mathrm{CP} is 3x+7y+4=0…3 x+7 y+4=0 \ldots (ii)

Solving (i) and (ii)

α=−4129,β=129∴17β−α=2\alpha=\frac{-41}{29}, \beta=\frac{1}{29} \quad \therefore 17 \beta-\alpha=2

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