Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • The locus of a point which divides the line segment joining the point and a point on the parabola,<img alt="x^{2}=4y," src="https://learn.careers360.com/latex-image/?x%5E

The locus of a point which divides the line segment joining the point (0,-1) and a point on the parabola,x^{2}=4y, internally in the ratio 1:2, is :
Option: 1 9x^{2}-12y=8
Option: 2 4x^{2}-3y=2
Option: 3 x^{2}-3y=2
Option: 4 9x^{2}-3y=2
 

Answers (1)

best_answer

 

 

Section Formula -

Section Formula

  1. Internal division

The coordinates of the point P (x, y) dividing the line segment joining the two points A (x1, y1) and B  (x2, y2) internally in the ratio m : n is given by 

\\\mathrm{\mathbf{x=\frac{mx_2+nx_1}{m+n},\;\;y=\frac{my_2+ny_1}{m+n}}}

-

 

 

Locus and its Equation -

Locus and its Equation

When point move in a plane under certain geometrical conditions, then the point traces out a path, This path of the moving point is known as a locus.   

For example, let a point O(0,0) is a fixed point (i.e. origin) and a variable point P (x, y) is in the same plane. If point P moves in such a way that the distance OP is constant r, then point P traces out a circle whose center is O(0, 0) and radius is r.

  
 

Steps to Finding the Equation of Locus

  1. Consider the point (h, k) whose locus is to be found.

  2. Express the given condition as an equation in terms of the known quantities and unknown parameters.

  3. Eliminate the parameters so that eliminant consists only locus coordinates h, k, and known quantities.

  4. Now, replace the locus coordinate (h, k) with (x, y) in eliminant.

-

\text { Let point } P \text { be }\left(2 t, t^{2}\right) \text { and } Q \text { be }(h, k)

\begin{array}{l}{h=\frac{2 t}{3}, k=\frac{-2+t^{2}}{3}} \\\\ {\text {Hence locus is } 3 k+2=\left(\frac{3 h}{2}\right)^{2} \Rightarrow 9 x^{2}=12 y+8}\end{array}

Correct Option (1)

Posted by

Kuldeep Maurya

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2025 schedule out for session 1; paper 1 from January 22
anam-khan

JEE Main 2025: NIT Tiruchirappalli saw stable preference in Civil Engineering cut-offs; 3 year trend analysis
anam-khan

JEE Main 2025: Grabbing BTech CSE seat at NIT tougher for economically weaker aspirants

Latest Question