Find The Equation Of The Locus Of A Moving Point So That Its Distance From The Point (1, 0) Is Always Twice The Distance From The Point (0, –2).

Why Kaysons ?

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.

Live Doubt Clearing Session

Ask your doubts live everyday Join our live doubt clearing session conducted by our experts.

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.

SPEAK TO COUNSELLOR ? CLICK HERE

Question

Find the equation of the locus of a moving point so that its distance from the point (1, 0) is always twice the distance from the point (0, –2).

Solution

Correct option is

3x2 + 3y2 + 2x + 16y + 15 = 0

Let (x1y1) be the coordinates of the moving point whose locus is to be found.

distance from (1, 0) = 2 × (distance from (0, –2))  

Replace x1 by x and y1 by y

Hence 3x2 + 3y2 + 2x + 16y + 15 = 0 is the equation of locus.

SIMILAR QUESTIONS

Q1

The number of integer values of m, for which the x-co-ordinate of the point of intersection of the lines 3x + 4y = 9 and y = mx + 1 is also an integer, is:

Q2

The vertices of a triangles are A (x1x1 tan α), B (x2x2 tan β) and C (x3,x3 tan γ). If the circumcentre of Δ ABC coincides with the origin and H (ab) be its orthocenter, then a/b is equal to:

Q3

A straight line L with negative slope passes through the point (8, 2) and cuts the positive coordinates axes at points P and Q. As L varies, the absolute minimum values of OP + OQ is (O is origin)

 

 

Q4

Consider the family of lines 

           (x + y – 1) + λ (2x + 3y – 5) = 0

and   (3x + 2y – 4) + µ (x + 2y – 6) = 0  

equation of a straight line that belongs to both the families is:

Q5

If p1p2p3 be the length perpendicular from the points

(m2, 2m), (mm’m + m’) and (m’2, 2m’)

respectively on the line  

               

Q6

The point (a2a + 1) is a point in the angle between the lines 3x – y + 1 = 0 and x + 2y – 5 = 0 containing origin. Then ‘a’ belongs to the interval. 

Q7

Find all points on x + y = 4 that lie at a unit distance from the line 4x + 3y– 10 = 0.

Q8

Find the equation of the obtuse angle bisector of the lines 12x – 5y + 7 = 0 and 3y – 4x – 1 = 0.

Q9

Find the bisector of the acute angle between the line 3x + 4y = 11 and 12x – 5y = 2. 

Q10

A straight line drawn through point A (2, 1) making an angle π/4 with the +X-axis intersects another line x + 2y + 1= 0 in point B. Find the length AB.