WebOct 5, 2024 · The focus of the parabola is the point (a, 0). Directrix: An imaginary line drawn parallel to the y-axis and passing through (-a, 0) is a directrix. Parabolas have parabolas that are perpendicular to their axes. Focal Chord: A focal chord is a chord that passes through the focus of a parabola. This chord passes through a parabola at two … 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.
Parabola: Equation, Formula, Graph, Derivation, and Properties
WebThe axis of parabola y 2 = 4 a x is X-axis and focus is (a, 0) Equation of line passing through ( a , 0 ) and making and angle θ with X-axis is y = t a n θ ( x − a ) Let this line intersect the parabola at ( x 1 , y 1 ) and ( x 2 , y 2 ) WebThe focal chord cuts the parabola at two distinct points. Focal Distance: The distance of a point \((x_1, y_1)\) on the parabola, from the focus, is the focal distance. The focal … cid hormus
Find the length of the chord of the parabola ${y^2} = 8x$, …
WebMar 4, 2024 · I assumed (accidentally and also correctly) that the chord was the diameter, knowing the centre was $(1,2)$ and I found the other vertex as $(2,4)$ and solved the question getting the correct answer. Is there perhaps a generalised method to find the equation of the parabola and the circle? 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 … Web∵ axis of the parabola bisects the P Q and tangents drawn to the ends of the chord are perpendicular ∴ P Q is the latusrectum of the given parabola whose focus is (3 2, − 1 2). Hence tangents will intersect at (1, − 2) ∵ directrix is parallel to latusrectum ∴ Slope of directrix = slope of tangent at vertex = − 1 3 and Slope of ... cid hipoferritinemia