Question

Find the radius of Curvature at the point(2,3) on the curve 9x
2 + 4y
2 = 36x.

Answer 1

Answer:

Radius of curvature is (2,0)

Step-by-step explanation:

9x^2+4y^2=36. (x^2/4)+(y^2/9)=1. therefore,(x^2/(2^2))+(y^2/(3^2)=1 comparing with standard form of an ellipse:((x-h)^2/a^2)+(y-k)^2=1. a=2,b=3,h=k=0.since,a<b therefore,It is a vertical ellipse.vertex of an ellipse:(h,k+b) and (h,k-b)=(0,3) and (0,-3).Ellipse cuts the X-axis at (-2,0) and (2,0) centre:(0,0). Radius of curvature at (2,0)(hence,it is a vertical ellipse).