﻿   Find the equations of the two circles which intersect the circles         x2 + y2 – 6y + 1 = 0 and x2 + y2 – 4y + 1 = 0   Orthogonally and touch the line 3x + 4y + 5 = 0.    : Kaysons Education

Find The Equations Of The Two Circles Which Intersect The Circles         x2 + y2 – 6y + 1 = 0 And x2 + y2 – 4y + 1 = 0   Orthogonally And Touch The Line 3x + 4y + 5 = 0.

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

Let the required circle be

x2 + y2 + 2gx + 2fy + c = 0            …(1)

and given circles are     x2 + y2 – 6y +1 = 0                        …(2)

and                                x2 + y2 – 4y + 1 = 0                       …(3)

Since (1) cuts (2) and (3) orthogonally

Solving (4) and (5), we get

= 0 and c = –1

Centre and radius of (6) are (–g, 0) and  respectively.

Since 3x + 4y + 5 = 0 is tangent of (6), then length of perpendicular from (–g, 0) to this line = radius of circle

Equations of circles are from (6),

SIMILAR QUESTIONS

Q1

Find the locus of the pole of the line lx + my + n = 0 with respect to the circle which touches y-axis at the origin.

Q2

Examine if the two circles x2 + y2 – 2x – 4y = 0 and x2 + y2 – 8y – 4 = 0 touch each other externally or internally.

Q3

Find the equation of the circle passing through (1, 1) and the points of intersection of the circles

x2 + y2 + 13x – 3y = 0 and 2x2 + 2y2 + 4x – 7y – 25 = 0.

Q4

Find the equation of the circle passing through the point of intersection of the circles x2 + y2 – 6x + 2y + 4 = 0, x2 + y2 + 2x – 4y – 6 = 0 and with its centre on the line y = x.

Q5

Find the equation of the circle passing through the points of intersection of the circles x2 + y2 – 2x – 4y – 4 = 0 and x2 + y2 – 10x – 12y + 40 = 0 and whose radius is 4.

Q6

Find the equation of the circle through points of intersection of the circlex2 + y2 – 2x – 4y + 4 = 0 and the line x + 2y = 4 which touches the line x+ 2y = 0.

Q7

Find the circle whose diameter is the common chord of the circles x2 + y2+ 2x + 3y + 1 = 0 and x2 + y2 + 4x + 3y + 2 = 0.

Q8

Find the angle between the circles

Q9

Find the equation of the circle which cuts the circle x2 + y2 + 5x + 7y – 4 = 0 orthogonally, has its centre on the line x = 2 and passes through the point (4, –1).

Q10

Find the radical centre of circles x2 + y2 + 3x + 2y + 1 = 0,

x2 + y2 – x + 6y + 5 = 0 and x2 + y2 + 5x – 8y + 15 = 0. Also find the equation of the circle cutting them orthogonally.