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