Equations of two diameters of a circle are 2x-3y=5 and 3x-4y=7.

Question

Equations of two diameters of a circle are $2x-3y=5$ and $3x-4y=7$. A certain line intersects the circle at only one point $P(\alpha,\beta)$. Then $17\beta-\alpha$ is equal to \_\_\_\_\_\_\_\_.

Answer: 2

Accepted Answer

*(The specific tangent line named in the stem was corrupted beyond recovery in the source. The two diameters meet at the circle's centre: solving $2x-3y=5,\ 3x-4y=7$ gives centre $(1,-1)$. The stated answer is $2$.)*

Solutions · 1