Calendar: 1873-1874 Page 619

THE SCHOOL 619 Find the ultimate values of sin2 χ cos χ -f χ sin χ and of when χ fcos χ π when χ cot Prove that the equation to the tangent at the point of the curve is x- T- £-0 Find the locus of the feet of the perpendiculars from the origin on the tangent to the curve c4 10 Define the polar subtangent at any point of curve and d& prove that its length is equal to t3-- dr Find the rectilinear and circular asymptotes of the curve 2Θ α 2Θ π 11 Find the condition that the two curves a2 A2 y2 may touch each other and when they do touch find the equa- tions to the normals at the points of contact 12 Show how to find the asymptotes of algebraic curves Example a2 a3y 13 Trace the curves x--- lb sinl sin 40 14 Define the circle of curvature at any point of curve and find an expression for its radius