Advanced Mathematics Set 1

What is the radius of curvature at point (1, 2) of the curve 4x – y2 = 0?

Find the radius of curvature at any point of the curve y + ln (cos x) = 0.

Determine the radius of curvature at (4, 4) of the curve y2 – 4x = 0.

Find the radius of curvature of the curve x = y3 at (1, 1)

The chords of the ellipse 64x2 + 25y2 = 1600 having equal slopes of 1/5 are bisected by its diameter. Determine the equation of the diameter of the ellipse.

Find the acute angle that the curve y = 1 – 3x2 cut the x-axis.

Find the angle that the line 2y – 9x – 18 = 0 makes with the x-axis.

Find the equation of the tangent to the curve y = x + 2x1/3 through point (8, 12)

Find the slope of the line whose parametric equations are x = 4t + 6 and y = t – 1.

What is the slope of the curve x2 + y2 – 6x + 10y + 5 = 0 at (1, 0).