text: ﻿ Find the locus of a point that divides a chord of slope 2 of the parabola y2= 4x internally in the ratio 1: 2. : Kaysons Education
  
  # Find The Locus Of A Point That Divides A Chord Of Slope 2 Of The Parabola y2= 4x internally In The Ratio 1: 2.
  
  #### Video lectures
  
  Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.
  
  #### Online Support
  
  Practice over 30000+ questions starting from basic level to JEE advance level.
  
  #### National Mock Tests
  
  Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.
  
  #### Organized Learning
  
  Proper planning to complete syllabus is the key to get a decent rank in JEE.
  
  #### Test Series/Daily assignments
  
  Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.
  
  ## Question
  
  ### Solution
  
  Correct option is
  
  4x = 9y2 – 12y + 8
  
  be the end points of chord AB.
  
  Also let M ≡ (x1y1) be a point which divides AB internally in ratio 1: 2.
  
  It is given that slope of PQ = 2.
  
  As M divides PQ in 1 : 2 ratio, we get:
  
  we have t eliminate two variables t1 and t2 between (i), (ii) and (iii).
  
  From (i), put t2 = 1 – tin (iii) to get:
  
  On substituting the values of t1 and t2 in (ii), we get:
  
  Replacing x1 by x and y, we get the required locus as:
  
  4x = 9y2 – 12y + 8
  
  #### SIMILAR QUESTIONS
  
  Q1
  
  The point of intersection of the tangents drawn to the curve x2y = 1 – y at the points where it is meet by the curve xy = 1 – y is given by
  
  Q2
  
  The slope of the normal at the point with abscissa x = –2 of the graph of the function f (x) = | x2 – x | is
  
  Q3
  
  The tangent to the graph of the function y = f (x) at the point with abscissax = 1 form an angle of π/6 and at the point x = 2 an angle of π/3 and at the point x = 3 an angle of π/4. The value of
  
  Q4
  
  The equations of the tangents to the curve y = x4 from the point (2, 0) not on the curve, are given by
  
  Q5
  
  The value of parameter a so that line (3 – ax + ay + (a2n – 1) = 0 is normal to the curve xy = 1, may lie in the interval
  
  Q6
  
  A cylindrical gas container is closed at the top and open at the bottom; if the iron plate forming the cylindrical sides. The ratio of the height to diameter of the diameter of the cylindrical using minimum material for the same capacity is
  
  Q7
  
  The critical points of the function f (x) where
  
  Q8
  
  Find the abscissa of the point on the curve ay2 = x3, the normal at which cuts of equal intercept from the axes.
  
  Q9
  
  Find the condition that the curves; ax2 + by2 = 1 and a ‘x2 + b’ y2 = 1 may cut each other orthogonally (at right angles).
  
  Q10
  
  Find the acute angle between the curves
  
  at their points of intersection when x > 0.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: ﻿ Find the locus of a point that divides a chord of slope 2 of the parabola y2= 4x internally in the ratio 1: 2. : Kaysons Education
  
  # Find The Locus Of A Point That Divides A Chord Of Slope 2 Of The Parabola y2= 4x internally In The Ratio 1: 2.
  
  #### Video lectures
  
  Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.
  
  #### Online Support
  
  Practice over 30000+ questions starting from basic level to JEE advance level.
  
  #### National Mock Tests
  
  Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.
  
  #### Organized Learning
  
  Proper planning to complete syllabus is the key to get a decent rank in JEE.
  
  #### Test Series/Daily assignments
  
  Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.
  
  ## Question
  
  ### Solution
  
  Correct option is
  
  4x = 9y2 – 12y + 8
  
  be the end points of chord AB.
  
  Also let M ≡ (x1y1) be a point which divides AB internally in ratio 1: 2.
  
  It is given that slope of PQ = 2.
  
  As M divides PQ in 1 : 2 ratio, we get:
  
  we have t eliminate two variables t1 and t2 between (i), (ii) and (iii).
  
  From (i), put t2 = 1 – tin (iii) to get:
  
  On substituting the values of t1 and t2 in (ii), we get:
  
  Replacing x1 by x and y, we get the required locus as:
  
  4x = 9y2 – 12y + 8
  
  #### SIMILAR QUESTIONS
  
  Q1
  
  The point of intersection of the tangents drawn to the curve x2y = 1 – y at the points where it is meet by the curve xy = 1 – y is given by
  
  Q2
  
  The slope of the normal at the point with abscissa x = –2 of the graph of the function f (x) = | x2 – x | is
  
  Q3
  
  The tangent to the graph of the function y = f (x) at the point with abscissax = 1 form an angle of π/6 and at the point x = 2 an angle of π/3 and at the point x = 3 an angle of π/4. The value of
  
  Q4
  
  The equations of the tangents to the curve y = x4 from the point (2, 0) not on the curve, are given by
  
  Q5
  
  The value of parameter a so that line (3 – ax + ay + (a2n – 1) = 0 is normal to the curve xy = 1, may lie in the interval
  
  Q6
  
  A cylindrical gas container is closed at the top and open at the bottom; if the iron plate forming the cylindrical sides. The ratio of the height to diameter of the diameter of the cylindrical using minimum material for the same capacity is
  
  Q7
  
  The critical points of the function f (x) where
  
  Q8
  
  Find the abscissa of the point on the curve ay2 = x3, the normal at which cuts of equal intercept from the axes.
  
  Q9
  
  Find the condition that the curves; ax2 + by2 = 1 and a ‘x2 + b’ y2 = 1 may cut each other orthogonally (at right angles).
  
  Q10
  
  Find the acute angle between the curves
  
  at their points of intersection when x > 0.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The provided text is a solution to a math problem. It describes the process of finding the locus of a point that divides a chord of a given slope of a parabola internally in a specific ratio. The problem is solved step-by-step, and the final answer is given as the equation of the locus.
  
  1. **Document Description**: The document contains a math problem and its solution. The problem is to find the locus of a point that divides a chord of slope 2 of the parabola \( y^2 = 4x \) internally in the ratio 1:2. The solution involves using the properties of the parabola and the section formula to derive the equation of the locus.
  
  2. **Question and Answer**: The document contains both the question and the answer.
  
  **Label**: question-and-answer