If the tangent to the parabola at a point is also a tangent to the ellipse, then is equal to:

Question

If the tangent to the parabola  at a point  is also a tangent to the ellipse,  then  is equal to:

Canvas Classes · Accepted Answer

🧠 Reading the Question — One Line Is Tangent to Two Curves

Same idea as the previous problem: a single line is tangent to two different curves. The trick is to write the line in a form natural to one curve, then force the tangency condition on the other.

The parabola  is in the form  with , so . The tangent at the point  on the parabola is  (using the chord-of-contact / tangent formula for : tangent is ).

First concrete move: write this tangent in slope form: . So slope  and intercept . Then

More questions from this chapter

More questions from this chapter