JEE MAIN - Mathematics (2024 - 29th January Morning Shift - No. 23)
Equations 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
Explanation
Centre of circle is $$(1,-1)$$
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Equation of $$A B$$ is $$7 x-3 y+10=0 \ldots$$ (i)
Equation of $$\mathrm{CP}$$ is $$3 x+7 y+4=0 \ldots$$ (ii)
Solving (i) and (ii)
$$\alpha=\frac{-41}{29}, \beta=\frac{1}{29} \quad \therefore 17 \beta-\alpha=2$$
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