Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 11-science Answered

IF a BE THE ANGLE SUBTENDED AT THE FOCUS BY THE NORMAL CHORD AT THE POINT(w,w),w#0  ON 
THE PARABOLA y^2=4x, THEN EQUATION OF THE LINE THROUGH (1,2)AND MAKING AN ANGLE a WITH
THE x-AXIS IS:
Asked by Sunil Soni | 17 Oct, 2015, 10:23: PM
answered-by-expert Expert Answer
begin mathsize 11px style Slope space of space tangent space to space straight y squared equals 4 straight x space is space 2 over straight y Hence comma space slope space of space normal space is space minus straight y over 2. If space left parenthesis straight w comma space straight w right parenthesis space is space straight a space point space on space this space parabola comma space then space straight w squared equals 4 straight w rightwards double arrow straight w equals 4 space space left parenthesis because space straight w not equal to 0 right parenthesis Slope space of space normal space at space left parenthesis 4 comma space 4 right parenthesis space is space minus 4 over 2 equals negative 2 Equation space of space normal space at space left parenthesis 4 comma 4 right parenthesis space is space straight y minus 4 equals negative 2 open parentheses straight x minus 4 close parentheses rightwards double arrow straight y equals negative 2 straight x plus 12 To space find space the space coordinates space of space other space end space of space the space normal space chord comma form space combined space equation space of space the space normal space with space the space equation space of space parabola. open parentheses negative 2 straight x plus 12 close parentheses squared equals 4 straight x rightwards double arrow open parentheses straight x minus 6 close parentheses squared equals straight x rightwards double arrow straight x squared minus 13 straight x plus 36 equals 0 rightwards double arrow straight x subscript 1 plus straight x subscript 2 equals 13 One space end space of space the space normal space chord space has space straight X minus coordinate space 4. Hence comma space the space straight X minus coordinate space of space the space other space end space is space 9. straight Y space coodinate space of space this space point space is space found space by space substituting space straight X space value space in space equation space of space normal. straight y equals negative 2 cross times 9 plus 12 rightwards double arrow straight y equals negative 6 Hence comma space the space coordinates space of space two space ends space of space the space normal space chord space are left parenthesis 4 comma 4 right parenthesis space and space left parenthesis 9 comma space minus 6 right parenthesis. Focus space of space the space parabola space straight y squared equals 4 straight x space is space left parenthesis 1 comma space 0 right parenthesis Slope space of space line space joining space left parenthesis 4 comma 4 right parenthesis space and space left parenthesis 1 comma space 0 right parenthesis space is space straight m subscript 1 equals fraction numerator 4 minus 0 over denominator 4 minus 1 end fraction equals 4 over 3 Slope space of space line space joining space left parenthesis 9 comma space minus 6 right parenthesis space and space left parenthesis 1 comma space 0 right parenthesis space is space straight m subscript 2 equals fraction numerator negative 6 minus 0 over denominator 9 minus 1 end fraction equals negative 6 over 8 equals negative 3 over 4 Here space straight m subscript 1 straight m subscript 2 equals negative 1. space So comma space the space normal space chord space subtends space right space angle space at space focus. straight a equals 90 to the power of straight o Hence comma space euqation space of space straight a space line space passing space through space left parenthesis 1 comma 2 right parenthesis space and space making space 90 to the power of straight o space with space straight X minus axis space is straight x equals 1 space left parenthesis parallel space to space straight Y minus axis space passing space through space left parenthesis 1 comma space 2 right parenthesis right parenthesis end style
Answered by satyajit samal | 18 Oct, 2015, 01:35: PM

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
CBSE 11-science - Maths
construction of Parabola When Distance between directrix and focus is given
Asked by praveenaditya843 | 22 Dec, 2023, 10:41: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
If PSQ is the focal chord of the parabola y^2=8x such that SP=6 then the length of SQ is  1)3 2)4 3)24
Asked by dineshchem108 | 21 Oct, 2018, 07:54: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
Find the vertex, focus, axis, diectrix x and latus rectum of the parabola.(a) y2 = 8x(b)y2 = -12x (c) x2 = 4y and (d) x2 = -16y.
Asked by Topperlearning User | 27 Feb, 2015, 01:28: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
Find the equation of the parabola whose focus is (3,0) and the vertex is (0.0).
Asked by Topperlearning User | 13 Nov, 2016, 05:55: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
Find the equation of the parabola whose focus is (4,0) and the directix x = -4.
Asked by Topperlearning User | 30 Apr, 2014, 11:27: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
Find the equation of the parabola with vertex (0,0) and focus (-5,0).
Asked by Topperlearning User | 30 Apr, 2014, 11:28: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
Find the equation of the parabola with V(0,0) and focus (0,-2).
Asked by Topperlearning User | 30 Apr, 2014, 11:29: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
Find the equation of the parabola with focus (0,4) and directix y = -4.
Asked by Topperlearning User | 30 Apr, 2014, 11:29: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
Find the equation of the parabola whose focus is (0,-7) and vertex is (0,0) 
Asked by Topperlearning User | 13 Nov, 2016, 05:54: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
Find the equation of the parabola with vertex (0,0), passing through the point (4,5) and symmetric about the x - axis.
Asked by Topperlearning User | 27 Feb, 2015, 01:20: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Get Latest Study Material for Academic year 24-25 Click here
×