Let the quadratic curve passing through the point and touching the line at be . Then the -intercept of the normal to the curve at the point in the first quadrant is .

Question

Let the quadratic curve passing through the point  and touching the line  at  be . Then the -intercept of the normal to the curve at the point  in the first quadrant is .

Canvas Classes · Accepted Answer

🧠 "Touching" is the Word You Should Notice

Read the question carefully. The curve "touches" the line  at . In Maths language, "touching" means TANGENT. So this single word gives us TWO conditions at once:
- The curve passes through .
- The slope of the curve at  equals the slope of the line, which is .

Combined with "passes through ", we have three conditions. A quadratic  has three unknowns. Three equations, three unknowns — the curve is determined.

So our first concrete move is: write thre

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