Let a circle passing through have its centre at the point . Let be the point of intersection of the lines and . If and , then the equation of the circle is :

Question

Let a circle passing through  have its centre at the point . Let  be the point of intersection of the lines  and . If  and , then the equation of the circle is :

Canvas Classes · Accepted Answer

🧠 Reading the Question — Limit Becomes the Tangent-Direction Approach

Two lines  and . At , both lines become  — they coincide. So the intersection  is indeterminate at . We need the limit as  — a typical "two lines collapsing to one, find the limit point" setup.

Approach: subtract  from  to get the difference line. Factor out , take the limit. The limiting line, combined with , gives the limit point.

🗺️ Working It Out

Subtract  from :

Divide by  (valid for ):

Take : the limiting

More questions from this chapter

More questions from this chapter