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Family of straight lines

A visitor wit...

Question

A visitor with sign board 'DO NOT LITTER' is moving on a circular path in an exhibition. During the movement, he stops at points represented by (3, -2) and (-2, 0). Also, centre of the circular path is on the line 2x - y = 3. What is the equation of the path? What message he wants to give in the public domain?

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Solution

$x^{2} + y^{2} + 3 x + 12 y + 2 = 0$ . Keep your place clean

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A person standing at the junction (crossing) of two straight paths represented by the equations $2 x - 3 y + 4 = 0$ and $3 x + 4 y - 5 = 0$ wants to reach the path whose equation is $6 x - 7 y + 8 = 0$ in the least time. Find equation of the path that he should follow.

Q. Question 4
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