The pole of the line lx+my+n 0
Webb30 dec. 2024 · Let (x1, y1) be the pole of line lx + my + n = 0. ...... (1) w.r.t. the ellipse x^2/a^2 + y^2/b^2 = 1 ...... (2) Now the polar of (x^1, y^1) w.r.t. (2) is x*x1/a^2 + y*y1/b^2 = 1 ...... (3) Since (1) and (3) represents the same polar, so comparing them we have (x1/a2)/l + (y1/b2)/b2 = (-1)/n or x1 = ( (-a^2)*l) /n and y1 = ( (-b^2)*m) /n .·. WebbTo find : Pole of line lx+my+n=0 wrt parabola y²=4ax.Sol. Let the pole be (p, q).Equation of polar of (p, q) wrt y²=4ax is T = 0, which isqy = 4a (x + p)/2 i.e. 2ax – qy + 2ap = 0 ....
The pole of the line lx+my+n 0
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Webb31 okt. 2024 · If the line lx + my + n = 0 is a normal to the parabola y2 = 4ax, then al3 + 2alm2 + m2 n = 0 parabola 1 Answer +1 vote answered Oct 31, 2024 by SudhirMandal (53.8k points) selected Nov 1, 2024 by faiz Best answer Suppose the line lx + my + n = 0 .... (1) is normal at (at2, 2at). However, at (at2, 2at), the equation of the normal is WebbFind the locus of the pole of the line lx+my+n=0 with respect to the circle which touches y -axis at the origin A y(x+n)=mx 2 B y(lx−n)=mx 2 C y(lx−n)=mx 2x 2 D none of these Medium Solution Verified by Toppr Correct option is D) Equation of variable circle which touch the y-axis at origin is x 2+y 2+λx=0 Let the pole of the above circle be P(h,k)
http://www.quizsolver.com/blog/view/details/IIT-JEE/Basic-Concepts-Of-Straight-line-Part-6/296/ WebbSolution: Tangent of the parabola y2=4axat point P(x1 ,y1 )isyy1 =2a(x+x1 )⇒2ax1 −yy1 +2ax=0… (i)which is also equation of the polar of the parabola y2=4axSame as the linelx+my+n=0… (ii)On comparing both lines, we getl2a =m−y =n2ax Taking first two parts(y=−l2am )Taking first and last parts,(x=ln )∴Required pole of the line is {ln ,l−2am }
Webb0 coins. Premium Powerups Explore Gaming. Valheim Genshin Impact Minecraft Pokimane Halo Infinite Call of Duty: Warzone Path of Exile Hollow Knight: Silksong Escape from Tarkov Watch Dogs: Legion. Sports. NFL NBA Megan Anderson Atlanta Hawks Los Angeles Lakers Boston Celtics Arsenal F.C. Philadelphia 76ers Premier League UFC. Webb5 apr. 2024 · Let the line be represented as L. So we have: ⇒ L: l x + m y + n = 0 We know that the center of the circle x 2 + y 2 = a 2 is at origin with a as its radius. Let the circle is cutting the line L at two different points A and …
Webb9 sep. 2024 · The equation of a line, whose segment between the lines 5x - y + 4 = 0 and 3x + 4y - 4 = 0 in bisected at the point (1, 5) is: Q4. The distance of the point P(4, 1) from the line 4x - y = 0 measured along the line making an …
WebbFind the locus of the pole of the line displaystyle: lx+my+n=0 with respect to the circle which touches y-axis at the origin Find the locus of the pole of the line lx+my+n = 0 l x + … simple soulful healthWebb20 apr. 2024 · The pole of the line l x + m y + n = 0 is ( − a 2 l n, − b 2 m n). (Ignoring for now the case n = 0 .) An arbitrary line through this point has an equation of the form λ n x + μ … rayco oilfield services \u0026 engineering pte ltdWebb15 apr. 2024 · Read Luxe Magazine - May/June 2024 Austin by Luxe Interiors + Design Magazine on Issuu and browse thousands of other publications on our platform. ... simple soul bucksportWebbTo find : Pole of line lx+my+n=0 wrt parabola y²=4ax.Sol. Let the pole be (p, q).Equation of polar of (p, q) wrt y²=4ax is T = 0, which isqy = 4a(x + p)/2 i.e. 2ax – qy + 2ap = 0 ....(1)Given eqn of polar is lx+my+n=0. ray cook 56 degree wedgeWebbUsing Article 267 of Loney's The elements of coordinate geometry, the equation of the normal of the given ellipse at P ( a cos ϕ, b sin ϕ) is. x ⋅ a sec ϕ − y ⋅ b csc ϕ + b 2 − a 2 = 0. So, l x + m y + n = 0 will be a normal if. l a sec ϕ = m − b csc ϕ = n b 2 − a 2. simple sorrows tribute storeWebbThe pole of the line lx + my + n = 0, (n ≠ 0) w.r.t. the ellipse S = 0 is IV. If the polar of P w.r.t. S = 0 passes through Q, then the polar of Q w.r.t. S = 0 passes through P. V. … simple sorry for your lossWebblx+my+n=0 with respect ot the hyperbola a 2x 2− b 2y 2=1. Then the equation of the polar is. a 2xx 1− b 2yy 1=1⋅⋅⋅⋅⋅⋅⋅⋅⋅(i) Since (x 1,y 1) is the pole of the line. lx+my+n=0⋅⋅⋅⋅⋅⋅⋅⋅⋅⋅(ii) … ray cook age 3-5