If the tangent to the curve, y = e x at a point (c, e c ) and the normal to the parabola, y 2 = 4x a

Q: JEE Main 2021 Conic Sections: If the tangent to the curve, y = e x at a point (c, e c ) and the normal to the parabola, y 2 = 4x a...

The correct answer is 0. **Key Concepts: Tangent and Normal to a Curve & X-intercept** Before diving into the solution, let's review the essential concepts that underpin this problem: 1. **Derivative as Slope:** For a curve defined by , the first derivative, (or ), gives the instantaneous rate of change of with respect to . Geometrically, this value represents the **slope of the tangent line** to the curve at any given point . 2. **Equation of the Tangent Line:** Once we have the slope of the tangent, , at a specific po

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If the tangent to the curve, y = e x at a point (c, e c ) and the normal to the parabola, y 2 = 4x at the point (1, 2) intersect at the same point on the x-axis, then the value of c is .

Accepted Answer

**Key Concepts: Tangent and Normal to a Curve & X-intercept** Before diving into the solution, let's review the essential concepts that underpin this problem: 1. **Derivative as Slope:** For a curve defined by , the first derivative, (or ), gives the instantaneous rate of change of with respect to . Geometrically, this value represents the **slope of the tangent line** to the curve at any given point . 2. **Equation of the Tangent Line:** Once we have the slope of the tangent, , at a specific point on the curve, we can write the

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