Focal chord length of parabola
WebMar 26, 2024 · Point of intersection in fourth quadrant gives me a ∈ [ 0, 1) So, parabola is y 2 = 4 ( a 2 − a + 1) x + 5 I know that length of focal chord is a ( t + 1 t) 2 for y 2 = 4 a x … WebLength of the focal chords of the parabola y 2=4ax at a distance p from the vertex is A p2a 2 B p 2a 2 C p 24a 3 D ap 2 Hard Solution Verified by Toppr Correct option is C) y 2=4ax …
Focal chord length of parabola
Did you know?
WebLength of the focal chords of the parabola y 2=4ax at a distance p from the vertex is A p2a 2 B p 2a 2 C p 24a 3 D ap 2 Hard Solution Verified by Toppr Correct option is C) y 2=4ax Slope of OP= Slope of OQ ⇒t 2= t 1−1 ∴ P(at 2,2at) & Q(t 2a, t−2a) Let length of focal chord be C. ∴ (at 2− t 2a)2+(2at+ t2a)2=C ⇒ a 2(t 2− t 21)2+(2a) 2(t+ t1)2=C WebApr 11, 2024 · The length of the focal chord which makes an angle θ with positive x-axis is 4a cosec 2 θ. Semi latus rectum is a harmonic mean between the segments of any focal …
WebThe length of a focal chord of the parabola y2 =4ax at a distance ‘b’ from the vertex is ‘c’, then A 2a2=bc B a3=b2c C b2 =ac D b2c=4a3 Solution The correct option is D b2c =4a3 … WebThe focal chord is a line segment that connects the focus of the parabola to the vertex of the parabola. The length of the focal chord is equal to the distance between the focus …
WebMar 27, 2024 · Point of intersection in fourth quadrant gives me a ∈ [ 0, 1) So, parabola is y 2 = 4 ( a 2 − a + 1) x + 5 I know that length of focal chord is a ( t + 1 t) 2 for y 2 = 4 a x with end end of focal chord being ( a t 2, 2 a t) Also, if the focal chord makes angle θ with x-axis then length of focal chord is 4 a csc 2 θ WebMar 14, 2024 · Consider a parabola y 2 = 4 a x , parameterize it as x = a t 2 and y = 2 a t, then it is found that if we have a line segment passing through focus, with each points having value of t as t 1 and t 2 for the parameterization, then it must be that: t 1 ⋅ t 2 = − 1 Hope for hints. conic-sections Share Cite Follow edited Mar 14, 2024 at 15:05
WebThe distance between the vertex and the focus, measured along the axis of symmetry, is the "focal length". The "latus rectum" is the chord of the parabola that is parallel to the directrix and passes through the focus. Parabolas can open up, down, left, right, or in some other arbitrary direction.
WebApr 11, 2024 · We are given a parabola \[{y^2} = 4ax\] Let us assume that the chord cuts the X-axis at point D(a,0) Then according to the question we are given the shortest distance from center to the chord is b. Length of the focal chord is c. The distance \[OD = a\]. Let us assume the focal chord makes an angle x with the X-axis. cooperative bank of kenya customer care lineWebFOCAL CHORD : A chord of the parabola, which passes through the focus is called a FOCAL CHORD. ... Also prove that CG = e2CN, where PN is the ordinate of P. x 2 y2 Q.16 Prove that the length of the focal chord of the ellipse 1 which is inclined to the major axis at a 2 b2 2ab 2 angle is . a 2 sin 2 b 2 cos2 ... family vacations in gatlinburgWebAssertion A: The least length of the focal chord of y 2 = 4 a x is 4 a. Reason R: Length of the focal chord of y 2 = 4 a x which makes an angle θ with its axis is 4 a cosec 2 θ . Medium cooperative bank of kenya kra pin numberWebApr 6, 2024 · Substitute the value you get in the expression of length of focal chord ‘c’ and get the value of c. Complete step-by-step answer: We have been given the equation of parabola as ${{y}^{2}}=4ax$ . We need to find the focal chord of the parabola at a distance p from the vertex. Let us take 2 points on the parabola as P and Q. cooperative bank of kenya fitch ratingWebSolution The correct option is A (8, –8) For the parabola y2 = 8x; focus S (2, 0). Given point is P (1 2,2) Slope of ←→ SP is 2−0 1 2−2 = −4 3 Equation to ←→ SP is4x+3y−8= 0 4x+3y−8= 0⇒ 4x=8−3y Substituting this value of 4x in y2 = 8x we get y2 = 2(8−3y) ⇒y2+6y−16−16 =0 ⇒(y+8)(y−2) = 0 ⇒ y= 2or−8 y =−8 ⇒4x =8−3(−8)= 32⇒ x= 8 ∴ point … family vacations in gaWebDec 8, 2024 · Question 4 :$$ $$ Let PQ be a focal chord of a parabola with origin as a focus . Coordinates of point P and Q be (-2,0) and (4,0) respectively . Find length of latus rectum and equation of tangent at vertex of parabola. cooperative bank of kenya exchange rateWebApr 6, 2024 · Length of focal chord c = 4 a 3 P 2. Hence, we got the required length as 4 a 3 P 2. Note: The length of a focal chord of a parabola varies inversely as the square of the distance from its vertex. If … cooperative bank of kenya/careers