Focal chord length of parabola
Web(v) Length of the focal chord having t 1 and t 2 as end points is a (t 1 — t 1) 2. (vi) Chord of contact drawn from a point (x 1, y 1) to the parabola y 2 = 4ax is yy 1, = 2a (x + x 1) (vii) Equation of the chord of the parabola y 2 = 4ax, which is bisected at (x 1 , y 1) is given by T = S 1 i.e. , yy 1 — 2a (x + x 1) = y 12 – 4ax WebDec 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.
Focal chord length of parabola
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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 Let the angle made by focal chord with x – axis be θ ∴ sinθ= b a Length of focal chord, c =4acosec2θ ⇒ c= 4a(a b)2 ⇒ b2c =4a3 Suggest Corrections 28 Similar questions Q. WebSimplifying gives us the formula for a parabola: x 2 = 4py In more familiar form, with " y = " on the left, we can write this as: \displaystyle {y}=\frac { {x}^ {2}} { { {4} {p}}} y = 4px2 where p is the focal distance of the parabola. Now let's see what "the locus of points equidistant from a point to a line" means.
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 WebFocal length calculated from parameters of a chord Suppose a chord crosses a parabola perpendicular to its axis of symmetry. Let the length of the chord between the points where it intersects the parabola be c and …
WebAssertion 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 WebPARABOLA ASSIGNMENT - Read online for free. Scribd is the world's largest social reading and publishing site. PARABOLA ASSIGNMENT. Uploaded by mynameis 1609. 0 ratings 0% found this document useful (0 votes) 0 views. 19 pages. Document Information click to expand document information.
WebApr 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.
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. can gas cause sharp pain under ribsWebNov 20, 2013 · This is the length of the focal chord (the "width" of a parabola at focal level). Let x 2 = 4 p y be a parabola. Then F ( 0, p) is the focus. Consider the line that passes through the focus and parallel to the directrix. Let A and A ′ be the intersections of the line and the parabola. Then A ( − 2 p, p), A ′ ( 2 p, p), and A A ′ = 4 p. Share Cite fitbit sense advanced smartwatch targetWebA parabola is the locus of a point that is equidistant from a fixed point called the focus (F), and the fixed-line is called the Directrix (x + a = 0). Let us consider a point P (x, y) on the … fitbit sense analog clock facesWebApr 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 … can gas cause sharp pain in left breast areaWebAssertion 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. can gas cause pain under sternumWebThe length of a focal chord of the parabola y 2=4ax at a distance b from the vertex is c. Then A 2a 2=bc B a 3=b 2c C ac=b 2 D b 2c=4a 3 Hard Solution Verified by Toppr Correct option is D) Equation of the focal line passing through (a,0) is y=m(x−a) The distance of this line from the vertex is b. ⇒b= ∣∣∣∣∣ 1+m 2am ∣∣∣∣∣ ⇒b 2(1+m 2)=a 2m 2 .... (1) can gas cause tightness in chest and throatWebThe extremities of a focal chord of the parabola y 2 = 4ax may be taken as the points t and –1/t. Length of the chord The abscissae of the points common to the straight line y = mx + c and the parabola y 2 = 4ax are given by the equation m 2 x 2 + (2mx – 4a) x + c 2 = 0. Length of the chord. As in the preceding article, the abscissae of the points … Buy Parabola Study Material (Mathematics) online for JEE Main/Advanced at … fitbit sense and iphone