Circle Question 6
Question 6 - 2024 (29 Jan Shift 1)
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
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Answer (2)
Solution
Centre of circle is $(1,-1)$
Equation of $A B$ is $7 x-3 y+10=0$
Equation of $\mathrm{CP}$ is $3 \mathrm{x}+7 \mathrm{y}+4=0$
Solving (i) and (ii)
$\alpha=\frac{-41}{29}, \beta=\frac{1}{29} \quad \therefore 17 \beta-\alpha=2$
