WebNote: If the chord joining the points t1 and t2 on the parabola y2 = 4ax is a focal chord then t1t2 = –1. Proof: Equation of the parabola is y2 = 4ax Focus S = (a, o) The equation of the chord is y(t1 + t2) = 2x + 2at1t2 If this is a focal chord then it passes through the focus (a, 0). ∴ 0 = 2a + 2at1t2 ⇒ t1t2 = –1. WebApr 7, 2024 · Any chord to ${{y}^{2}}=4ax$ which passes through the focus is called a focal chord of the parabola ${{y}^{2}}=4ax$. Focus can be defined as a point in parabola with coordinates $\left( a,0 \right)$. Consider a point P on the parabola whose coordinate in parametric form be $\left( a{{t}^{2}},2at \right)$. For the other extremity Q of the focal ...
Relation between end point of focal chord of parabola
WebOct 6, 2024 · The equation of the parabola is often given in a number of different forms. One of the simplest of these forms is: (x − h)2 = 4p(y − k) A parabola is defined as the locus (or collection) of points equidistant from a given point (the focus) and a given line (the directrix). Another important point is the vertex or turning point of the parabola. WebIf the feet A (a t 1 2 , 2 a t 1 ) and B (a t 2 2 , 2 a t 2 ) are the ends of a focal chord of the parabola, then the locus of P (h, k) is. Hard. View solution > The length of the intercept on the normal at the point (a t 2, 2 a t) of the parabola y 2 = 4 a x made by the circle which is described on the focal distance of the given point as ... how much is disney plus uk 2022
Parametric Co-ordinates of Parabola , Focal Chord of …
WebIit Jee Important Formula May 13th, 2024 - JEE Main Result 2024 will be Declared Today likely at 11 00 AM as per few reports for the online and offline JEE Main entrance exam … WebSince, focal chord of parabola y 2 = a x is 2 x − y − 8 = 0. Also, this chord passes through focus (4 a , 0) ∴ 4 2 a − 0 − 8 = 0 ⇒ a = 1 6 ∴ Directrix is x = − 4 ⇒ x + 4 = 0 Web25758 Points. 3 years ago. Dear student. focus of y^2 = 4x is (1,0) focal chord inclined at an angle of 45 degree from x axis. y – 0 = 1 (x- 1) y = x – 1. Hope it helps. how much is disney plus in uk