QUESTION: 13. or yy 1 – 2a(x + x 1) = y 1 2 – 4ax 1 or yy 1 – 2ax = y 1 2 – 2ax 1. So, p = at2/2 and q = at. an ellipse. If the parabola is Y 2 = 4ax take the focal chord which is easy for calculation e.x. Show that as the focal chord varies, the line PQ passes through a fixed point. a circle. 9. Illustration : Through the vertex O of a parabola y 2 = 4x chords OP and OQ are drawn at right angles to one another. B. Also find the locus of the middle point of PQ. Let the other end be a varaible point P given by (at2,2at). Let M(p,q) be the midpoint of the chord OP. y + tx = 2at + at 3. … (2) 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 (b) Focal chord : A chord of the parabola, which passes through the focus is called a focal chord. is Y^2=4aX(standard eq.) (Chords orthogonal at the vertex) Let PQ be a chord of a parabola with vertex O such that angle POQ is a right angle. The extremities of a focal chord of the parabola y 2 = 4ax may be taken as the points t and − 1/t. ... 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 … … (1) Equation of the chord with mid point (x 1, y 1) is T = S1. Equation of chord to the given parabola with given mid point (2,1) is given by, T = S 1 *Multiple options can be correct. a parabola. Locus of the mid–point of chord AB is (a) 22 2 2 4 22 xy ... 19. Let the parabola we consider and draw chords be y2 = 4ax. 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. Find the locus of the middle point of focal chord of parabola whose eq. For this parabola : (i) Vertex is (0,0). 8. points P and Q. Find the locus of the midpoint of PQ. The locus of the mid-points of the focal chord of the parabola y 2 = 4ax is. 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. Hence locus of (α, β) is y2 = 2a(x – a). Locus of midpoint of focal chord. Show that for all position of P, PQ cuts the axis of the parabola at a fixed point. Midpoint of OP is (at2/2,at). (c) Double ordinate : The Vertex is O(0.0), which is one end of the chord. The locus of the middle points of all chords of the parabola y 2 = 4ax passing through the vertex is. 1. This worksheet shows the locus of the midpoint of the focal chord of a parabola Find the locus of the middle points of the normal chords of the parabola y 2 = 4ax. (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. Then the midpoint of the chord PQ. 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. y 2 = a(x - a) y 2 = 2a(x - a) y 2 = 4a(x - a) None of these. Solution: Equation of the normal chord at any point (at 2, 2at) of the parabola is. a straight line. asked Nov 4, 2019 in Mathematics by SudhirMandal (53.5k points) parabola; 0 votes. Point P given by ( at2,2at ) ), which passes through the focus is called focal... Hence locus of the parabola y 2 = 4ax may be taken as the points t and − 1/t a! 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