Question

show that the radius of curvature of the curve y^2=a^2(a-x)/x at (a,0)is a/2​

Answer 1

Answer:

The equation of the curve, (a – x)y2 = (a + x)x2 passes through the origin. To see the nature of the tangent at the origin, equate to zero the lowest degree terms in x and y, i.e. ay2 = ax2 or y = ± x i.e., at the origin, neither of the axis are tangent to the given curve ∴ Putting or On comparing the coefficients of x2 and x3, we get ap2 = a ⇒ p = ± 1 and apq – p2 = 1 ⇒ q = ± 2/ a ∴ Hence ρ(0, 0) is numerically a√2. Alternately: Equation of the curve is ∴ i.e., so that and At (0, 0) y1 = ± 1, y2 = ± 2/a ∴ Hence ρ(0, 0) is numerically a√2Read more on Sarthaks.com - https://www.sarthaks.com/494766/show-that-the-radii-of-curvature-of-the-curve-y-2-x-2-a-x-a-x-at-the-origin-is-a2