Equations 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 _ _ _ _ _.

Coordinate Geometry: JEE Main 2024 Mathematics question

JEE Main 2024 · 29 Jan, Morning shift · Q34

JEE Main 202429 Jan, Morning shiftMathematicsMediumCoordinate Geometry478× since 2002

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 _________.

Your answerType your answer. Integers and decimals are accepted.