Let a parabola be such that its vertex and focus lie on the positive -axis at a distance and units from the origin, respectively. If tangents are drawn from to the parabola which meet at and ,

Question

Let a parabola  be such that its vertex and focus lie on the positive -axis at a distance  and  units from the origin, respectively. If tangents are drawn from  to the parabola  which meet  at  and , then the area (in sq. units) of  is equal to :

Canvas Classes · Accepted Answer

🧠 Chord of Contact from External Point — One Line, Then Intersect

Read the question. Vertex , focus , . Parabola: . Tangents from  meet the parabola at  and . Find the area of .

The cleanest tool here is the chord of contact. For tangents from external point  to , the chord of contact (line through the two touch-points  and ) is given by the -form:

.

For  and : -form gives , so .

So  and  lie on the vertical line . Plug into the parabola: , so . Hence  and .

🖼️ Visual Sketch

The parabol

More questions from this chapter

More questions from this chapter