Q. 35.0( 1 Vote )

# A point moves as so that the difference of its distances from (ae, 0) and (-ae, 0) is 2a, prove that the equation to its locus is , where b2 = a2(e2 – 1).

Key points to solve the problem:

• Idea of distance formula- Distance between two points A(x1,y1) and B(x2,y2) is given by- AB =

How to approach: To find locus of a point we first assume the coordinate of point to be (h, k) and write a mathematical equation as per the conditions mentioned in question and finally replace (h, k) with (x, y) to get the locus of point.

Let the point whose locus is to be determined be (h,k)

Distance of (h,k) from (ae,0) =

Distance of (h,k) from (-ae,0) =

According to question:

Squaring both sides:

Again squaring both sides:

where b2 = a2(e2 – 1)

Replace (h,k) with (x,y)

Thus, locus of a point such that difference of its distances from (ae, 0) and (-ae, 0) is 2a:

where b2 = a2(e2 – 1) ….proved

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Circulatory system53 mins
Examples of multi electronic systemFREE Class
Examples of odd electronic systemFREE Class
Centre of Mass Frame (C-Frame)59 mins
Moment of Inertia | Understanding the basicsFREE Class
Introduction to Rotation & Torque37 mins
Important Questions on Torque43 mins
Understand Parallel & Perpendicular Axis Theorem in detail40 mins
Questions based on rotational motion44 mins
Moment of Inertia | Some special casesFREE Class
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses