s and Normals. / 52. To find the equation of the tangent to the para-bola y- = 4:a.r in terms of the co-ordinates of the point ofcontact (y,y)- Let PQ be a secant through the points P(x. ij) andQ{3c, y) on the parabola y- = iax. The equation of the line through (x, y), (x, y) is X -x ^y -y x - ^ y… … Let now the point (x, y) move up indefinitely closeto {x,y)) then PQ becomes PT, the tangent at P;also y becomes y. and (2) becomes y-y =2^{^-^^) Hence yy = 2ax - 2ax + y^, = 2ax - 2ax + 4«a-, = 2(l{x + x);and yy = 2a(x + x) is the equation of the tangent tothe parabola y- = 4:ax, at the point…
Geometry, Analytic
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