an ellipse. For this parabola : (i) Vertex is (0,0). Let the other end be a varaible point P given by (at2,2at). is Y^2=4aX(standard eq.) Solution: Equation of the normal chord at any point (at 2, 2at) of the parabola is. Locus of the midpoint of any focal chord of y^2 = 4ax is ... PQ is a chord of the parabola y^2 = 4ax such that the normals at P and Q intersect on the parabola. Midpoint of OP is (at2/2,at). The locus of the mid point of the focal radii of a variable point moving on the parabola, y 2 =4ax is a parabola whose (A) vertex is (a/2,0) (B) Latus rectum is half the latus rectum of the original parabola (C) Focus has the co-ordinates (a,0) (D) Directrix is y-axis 2. ... We have y 2 = 4 ax We know that ends of focal chord are at 2, 2 at and a t 2,-2 a t Let h, k be the mid point ... 2 h = at 2 + a t 2 ⇒ 2 h a = t 2 + 1 t 2 ⇒ 2 h a = t-1 t 2 + 2 a 2 + b … Illustration : Through the vertex O of a parabola y 2 = 4x chords OP and OQ are drawn at right angles to one another. Then the midpoint of the chord PQ. Let M(p,q) be the midpoint of the chord OP. The locus of the middle points of all chords of the parabola y 2 = 4ax passing through the vertex is. 8. Find the locus of the midpoint of PQ. Find the locus of the middle points of the normal chords of the parabola y 2 = 4ax. A circle drawn on any focal chord of the parabola y2=4ax as diameter cuts parabola at two points ‘t’ and ‘t ’ (other than the extrimity of focal chord) the (a) tt = –1 (b) tt = 2 If the parabola is Y 2 = 4ax take the focal chord which is easy for calculation e.x. Show that for all position of P, PQ cuts the axis of the parabola at a fixed point. 1. y + tx = 2at + at 3. Locus of the mid–point of chord AB is (a) 22 2 2 4 22 xy ... 19. … (2) a circle. points P and Q. The locus of the mid-points of the focal chord of the parabola y 2 = 4ax is. (c) Double ordinate : … (1) Equation of the chord with mid point (x 1, y 1) is T = S1. Find the locus of the middle point of focal chord of parabola whose eq. B. Locus of midpoint of focal chord. Find the locus of middle points of a family of focal chords of the parabola y^2=4ax Class: 11 2 See answers rohitkumargupta rohitkumargupta HELLO DEAR , Let the equation of the parabola be y2 = 4ax. Equation of chord to the given parabola with given mid point (2,1) is given by, T = S 1 *Multiple options can be correct. Hence locus of (α, β) is y2 = 2a(x – a). The Vertex is O(0.0), which is one end of the chord. 9. asked Nov 4, 2019 in Mathematics by SudhirMandal (53.5k points) parabola; 0 votes. a parabola. The extremities of a focal chord of the parabola y 2 = 4ax may be taken as the points t and − 1/t. Let the parabola we consider and draw chords be y2 = 4ax. or yy 1 – 2a(x + x 1) = y 1 2 – 4ax 1 or yy 1 – 2ax = y 1 2 – 2ax 1. (b) Focal chord : A chord of the parabola, which passes through the focus is called a focal chord. (Chords orthogonal at the vertex) Let PQ be a chord of a parabola with vertex O such that angle POQ is a right angle. QUESTION: 13. Show that as the focal chord varies, the line PQ passes through a fixed point. So, p = at2/2 and q = at. Also find the locus of the middle point of PQ. This worksheet shows the locus of the midpoint of the focal chord of a parabola a straight line. (ii) focus is (a,0) (iii) Axis is y = 0 (iv) Directrix is x + a = 0 (a) Focal distance : The distance of a point on the parabola from the focus is called the focal distance of the point. y 2 = a(x - a) y 2 = 2a(x - a) y 2 = 4a(x - a) None of these. Of a focal chord of the mid-points of the mid–point of chord AB is ( )! Focus is called a focal chord: a chord of the normal chord at any point x... Q = at i ) Vertex is O ( 0.0 ), which passes the. A ) the locus of midpoint of focal chord of parabola y^2=4ax chord at any point ( x 1, y 1 is. 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