﻿ Let P be a point on the ellipse , 0 < b < a. Let the line parallel to y-axis passes through P meet the circle  at the point Q, such that P and Q are the same side of x-axis. For two positive  real numbers r and s, find the locus of the point Ron PQ such that PR : RQ = r : s as P varies over the ellipse.   : Kaysons Education

# Let P be A Point On The Ellipse , 0 < b < a. Let The Line Parallel To Y-axis Passes Through P meet The Circle  at The Point Q, Such That P and Q are The Same Side Of X-axis. For Two Positive  real Numbers r and s, Find The Locus Of The Point Ron PQ such That PR : RQ = r : s as P Varies Over The Ellipse.

#### 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

Given   PR : RQ = r : s

Hence locus of R is

#### SIMILAR QUESTIONS

Q1

For what value of λ dose the line y = x + λ touches the ellipse

9x2 + 16y2 = 144.

Q2

Find the equations of the tangents to the ellipse  which are perpendicular to the line y + 2x = 4.

Q3

Find the locus of the foot of the perpendicular drawn from centre upon any tangent to the ellipse .

Q4

Find the locus of the points of the intersection of tangents to ellipse  which make an angle θ.

Q5

Find the locus of the poles of tangents to  with respect to the concentric ellipse .

Q6

Determine the equation of major and minor axes of the ellipse

Also, find its centre, length of the latusrectum and eccentricity.

Q7

Find the locus of the centroid of an equilateral triangle inscribed in the ellipse

Q8

If SY and S1Y1 be perpendiculars from the foci upon the tangent atP of an ellipse, then Y and Y1 lie on the auxiliary circle andSY.S1Y1 =

Q9

Find the condition on a and b for which two distinct chords of the ellipse  passing through (a, –b) are bisected by the line x + y = b

Q10

Consider the family of circle x2 + y2 = r2, 2 < r < 5. If in the first quadrant the common tangent to a circle of the family and the ellipse 4x2 + 25y2 = 100 meets the coordinate axes at A and B, then find the equation of the locus of the mid point of AB.