©G Dear2008 – Not to be sold/Free to use Mathematic (Preliminary) Locus and the Parabola Tangent and Normal Stage 6 - Year 11 Press Ctrl-A ©G Dear2008 – Not to be sold/Free to use

To find the equation of the tangent of x2 = 4y at ( 6, 9). Parabola as a locus The Tangent To find the equation of the tangent of x2 = 4y at ( 6, 9). Tangent Normal y = x2 4 Make y the subject dy = 2x = x dx 4 2 Differentiate to find the gradient. (x = 6) m = 6 = 3 2 Find the equation of the tangent y – y1 = m(x – x1) 3x – y – 9 = 0 y – 9 = 3(x – 6) y – 9 = 3x – 18 3x – y – 9 = 0

To find the equation of the normal of x2 = 4y at ( 6, 9). Parabola as a locus Normals Tangent Normal To find the equation of the normal of x2 = 4y at ( 6, 9). x + 3y – 33 = 0 Gradient of tangent m = 3 m2 = -1 m1 = -1 3 Gradient of normal Find the equation of the normal y – y1 = m(x – x1) y – 9 = -1(x – 6) 3 -3y + 27 = x – 6 x + 3y – 33 = 0