Let a line , intersect the parabola, , at a point , other than the origin. Let the tangent to it a , meet the -axis at the point . If area square unit, then is equal to

Question

Let a line , intersect the parabola, , at a point , other than the origin. Let the tangent to it a , meet the -axis at the point . If area  square unit, then  is equal to

Canvas Classes · Accepted Answer

🧠 Line Meets Parabola + Tangent at That Point — Form a Triangle, Solve for

Read the question. The line  () meets  at  (not the origin). Tangent at  meets the -axis at . Area of  = 4. Find .

Substitute  into : , so  (origin) or . So .

For  (), tangent at : . So , giving .

At : . So .

🖼️ Visual Sketch

The parabola  opens to the right with vertex at origin. The line  (positive slope) passes through origin and crosses the parabola at  in the first quadrant. The tangent at  slopes more gentl

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More questions from this chapter