Home
Class 11
MATHS
Find the equation of the circle passing ...

Find the equation of the circle passing through the points (4,1) and (6,5) and whose centre lies on the line 4x+ y = 16.

Text Solution

Verified by Experts

Let equation of circle be
`x^(2)+y^(2)+2gx+2fy+c=0`
This circle passes through the point (4,1).
`:.4^(2)+1^(2)+2(4)+2f(1)+c=0`
`rArr" "8g+2f+c=-17` . . . (1)
Given circle passes through the point (6,5).
`:.6^(2)+5^(2)+2g(6)+2f(5)+c=0`
`rArr" "12g+10f+c=-61` . . . (2)
The centre (-g,-f) of circle lies on the line
4x+y=16
`:.` -4g-f=16 . . . (3)
Subtracting equation (1) from equation (2),
4g+8f=-44 . . . (4)
Adding equations (3) and (4),
7f=-28
`rArr" "f=-4`
Put the value of f in equation (3)
-4g+4=16
`rArr" "-4g=12`
`rArr" "-4g=12`
`rArr" "g=-3`
Put the of g and f in equation (1)
-24-8+c-17
`rArr" "c=15`
Therefore equation of circle is
`x^(2)+y^(2)-6x-8y+15=0`
Promotional Banner

Topper's Solved these Questions

  • CONIC SECTION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 11.2|12 Videos

  • CONIC SECTION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 11.3|20 Videos

  • CONIC SECTION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 11G|10 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATION

    NAGEEN PRAKASHAN ENGLISH|Exercise MISCELLANEOUS EXERCISE|20 Videos

  • INTRODUCTION OF THREE DIMENSIONAL GEOMETRY

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|6 Videos

Similar Questions

Explore conceptually related problems

Find the equation of the circle passing through the points (0, -1) and (2, 0) and whose centre lies on the line 3x+y=5

Find the equation of circle passing through the points (0,5) and (6,1) and whose centre lies on the line 2x+5y=25.

Find the equation of circle passing through the point (2,3) and (-1,1) and whose centre is on the line x - 3y - 11 = 0

Find the equaiton of the circle passing through the points (2, -3) and (3, -2) and whose centre lies on the line 2x-3y=8 .

Find the equation of the circle which passes through the points (5,0) and (1,4) and whose centre lies on the line x + y - 3 = 0.

Find the equation of a circle passing through the points (-1,5) and (-7,5) and its centre lies on the line 3x+4y+8=0.

Find the equation of the circle which passes through the points (-1,2) and (3,-2) and whose centre lies on the line x-2y=0 .

Find the equation of the circle which passes through the points (2,""""-2) , and (3,4) and whose centre lies on the line x+y=2 .

Find the equation of the circle passing through the point (7,3) having radius 3 units and whose centre lies on the line y=x-1

Find the equation of the circle passing through the point: (1,2) , (3,-4) and (5,-6) .