Home
Class 12
MATHS
The locus of the center of the circle su...

The locus of the center of the circle such that the point (2, 3) is the midpoint of the chord `5x+2y=16` is (a)`2x-5y+11=0` (b) `2x+5y-11=0` (c)`2x+5y+11=0` (d) none of these

A

`2x-5y+11=0`

B

`2x+5y-11=0`

C

`2x+5y+11=0`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
1

Slope of the given line `= - (5)/(2)`
`:. (-(5)/(2))((3+f)/(2+g))=-1`
or `15+5f=4+2g`
Therefore, the locus is `2x-5+11=0`
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    CENGAGE PUBLICATION|Exercise Multiple Correct Anser Type|29 Videos

  • CIRCLE

    CENGAGE PUBLICATION|Exercise Linked Comprehension Type (For Problem 1-3)|3 Videos

  • CIRCLE

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 4.17|2 Videos

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Comprehension|11 Videos

  • CIRCLES

    CENGAGE PUBLICATION|Exercise Comprehension Type|8 Videos

Similar Questions

Explore conceptually related problems

The locus of the center of the circle touching the line 2x-y=1 at (1,1) is (a) x+3y=2 (b) x+2y=2 (c) x+y=2 (d) none of these

The locus of the image of the point (2,3) in the line (x-2y+3)+lambda(2x-3y+4)=0 is (lambda in R) (a) x^2+y^2-3x-4y-4=0 (b) 2x^2+3y^2+2x+4y-7=0 (c) x^2+y^2-2x-4y+4=0 (d) none of these

One end of a diameter of the circle x^2+y^2-3x+5y-4=0 is (2,1). Find the coordinates of the other end.

From the points (3, 4), chords are drawn to the circle x^2+y^2-4x=0 . The locus of the midpoints of the chords is (a) x^2+y^2-5x-4y+6=0 (b) x^2+y^2+5x-4y+6=0 (c) x^2+y^2-5x+4y+6=0 (d) x^2+y^2-5x-4y-6=0

The combined equation of the asymptotes of the hyperbola 2x^2+5x y+2y^2+4x+5y=0 is (a) 2x^2+5x y+2y^2+4x+5y+2=0 (b) 2x^2+5x y+2y^2+4x+5y-2=0 (c) 2x^2+5x y+2y^2=0 (d) none of these

The equation of the locus of the middle point of a chord of the circle x^2+y^2=2(x+y) such that the pair of lines joining the origin to the point of intersection of the chord and the circle are equally inclined to the x-axis is (a) x+y=2 (b) x-y=2 (c) 2x-y=1 (d) none of these

From any point P lying in the first quadrant on the ellipse (x^2)/(25)+(y^2)/(16)=1,P N is drawn perpendicular to the major axis and produced at Q so that N Q equals to P S , where S is a focus. Then the locus of Q is (a) 5y-3x-25=0 (b) 3x+5y+25=0 (c) 3x-5y-25=0 (d) none of these

The center of a rectangular hyperbola lies on the line y=2xdot If one of the asymptotes is x+y+c=0 , then the other asymptote is: (a) 6x+3y-4c=0 (b) 3x+6y-5c=0 (c) 3x-6y-c=0 (d) none of these

Tangents P A and P B are drawn to x^2+y^2=9 from any arbitrary point P on the line x+y=25 . The locus of the midpoint of chord A B is (a) 25(x^2+y^2)=9(x+y) (b) 25(x^2+y^2)=3(x+y) (c) 5(x^2+y^2)=3(x+y) (d) none of these

If the foci of a hyperbola lie on y=x and one of the asymptotes is y=2x , then the equation of the hyperbola, given that it passes through (3, 4), is (a) x^2-y^2-5/2x y+5=0 (b) 2x^2-2y^2+5x y+5=0 (c) 2x^2+2y^2-5x y+10=0 (d) none of these

CENGAGE PUBLICATION-CIRCLE -Excercises (Single Correct Answer Type)
  1. In triangle A B C , the equation of side B C is x-y=0. The circumcente...

    Text Solution

    |

  2. A rhombus is inscribed in the region common to the two circles x^2+y^2...

    Text Solution

    |

  3. The locus of the center of the circle such that the point (2, 3) is ...

    Text Solution

    |

  4. Consider a family of circles which are passing through the point (-1,1...

    Text Solution

    |

  5. The line 2x-y+1=0 is tangent to the circle at the point (2, 5) and the...

    Text Solution

    |

  6. A right angled isosceles triangle is inscribed in the circle x^2 + y^2...

    Text Solution

    |

  7. f(x , y)=x^2+y^2+2a x+2b y+c=0 represents a circle. If f(x ,0)=0 has e...

    Text Solution

    |

  8. The equation of the circumcircle of an equilateral triangle is x^2+y^2...

    Text Solution

    |

  9. If it is possible to draw a triangle which circumscribes the circle (...

    Text Solution

    |

  10. The locus of the centre of the circle(xcos alpha + y sin alpha - a)^2 ...

    Text Solution

    |

  11. about to only mathematics

    Text Solution

    |

  12. A B C D is a square of unit area. A circle is tangent to two sides of ...

    Text Solution

    |

  13. A circle of constant radius a passes through the origin O and cuts the...

    Text Solution

    |

  14. The circle x^2+y^2=4 cuts the line joining the points A(1, 0) and B(3,...

    Text Solution

    |

  15. If a circle of radius R passes through the origin O and intersects the...

    Text Solution

    |

  16. (6, 0), (0, 6) and (7, 7) are the vertices of a triangle. The circle i...

    Text Solution

    |

  17. If O is the origin and O Pa n dO Q are the tangents from the origin to...

    Text Solution

    |

  18. about to only mathematics

    Text Solution

    |

  19. If the conics whose equations are S-=sin^2thetax^2+2h x y+cos^2thetay^...

    Text Solution

    |

  20. From a point R(5, 8) two tangents RP and RQ are drawn to a given circl...

    Text Solution

    |