Question

Q.3
The radius of curvature at (3,-4) to the curve is x2 + y2 = 25
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Answer 1

Answer:

5 is Really Right Answer but for only Curvature is 1/5

Answer 2

Given,

The curve x² + y² = 25 is given along with the point (3,-4).

To find,

We have to find the radius of curvature 'ρ' for the given curve.

Solution,

The radius of curvature for the curve x² + y² = 25 is 5.

We can simply find the radius of the curvature by using the formula

  ρ = (1+y₁²)³/₂ / y₂

Differentiating the equation of the curve w.r.t. x

    2x + 2y . y₁ = 0

            2y . y₁ = -2x

                   y₁ = -x/y         (1)

                  y₁ = 3/4

Again differentiating equation (1) w.r.t. x

          y₂ = -y +x.y₁/y²               (2)

          y₂ = 25/64

           ρ = (1+y₁²)³/₂ / y₂

           ρ = (1 + 9/16)³/₂ / 25/64

            ρ = 5

Hence, the radius of curvature at (3,-4) to the curve x² + y² = 25 is 5.