Equation of two diameters of a circle are 2 x-3 y=5 and 3 x-4 y=7 . The line joining the points (-22/7,-4 ) and (-1/7, 3 ) intersects the circle at only one point P(α, β) . Then 17 β-α is equal to

Mathematics · Circles

JEE Main 2024 — 29 January, Shift 1 — Question 20

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

Answer: 2

Numerical answer — enter this value.

Step-by-step solution

Centre of circle is $(1,-1)$ Equation of AB is

$7 \mathrm{x}-3 \mathrm{y}+10=0 \ldots$ (i)

Equation of CP is $3 x+7 y+4=0 \ldots$ (ii)

Solving (i) and (ii) $\alpha=\frac{-41}{29}, \beta=\frac{1}{29}$

$\therefore 17 \beta-\alpha=2$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 29 January, Shift 1
Subject: Mathematics
Chapter: Circles
Topic: Considering a Line or a Point wrt a Circle