• Lines L1 and L2 are perpendicular.
• P is the point of intersection.
• A lies on L1, B lies on L2.
• Isosceles triangles have two equal length sides.
• You have just worked out the length of AP squared in the previous question.
• As shown, B could lie in two possible positions for the length of AP to equal the length of BP.
In order to work out the two possible positions, use the line equation of L2 to work out the position vector OB in terms of mu. Then work out the vector PB (or BP) in terms of mu.
Use this information to form a quadratic equation in terms of mu to find the length of BP (or PB), setting it equal to AP squared (as the two lengths are equal).
Does this help? I can write a solution if needs be.
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