Home
Class 12
MATHS
A circle with center in the first quadra...

A circle with center in the first quadrant is tangent to `y = x+10, y = x - 6`, and the `y- a x is`. Let `(h, k)` be the center of the circle. If the value of `(h + k) = a + b sqrta` where `sqrta` is a surd, find the value of `a +b`.

Text Solution

Verified by Experts

The correct Answer is:
10
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    MOTION|Exercise Exercise - 3 (Subjective | JEE Advanced) Matrix Match Type|1 Videos

  • CIRCLE

    MOTION|Exercise Exerise - 4 | Level - I (Previous Year|JEE Main|10 Videos

  • CIRCLE

    MOTION|Exercise Exercise -2 (Level - II) Multiple correct | JEE Advanced|14 Videos

  • BINOMIAL THEOREM

    MOTION|Exercise Exercise -4 (Level - II) ( Previous Year )|7 Videos

  • COMPLEX NUMBER

    MOTION|Exercise EXERCISE - 4 (LEVEL -II) PREVIOUS YEAR - JEE ADVANCED|33 Videos

Similar Questions

Explore conceptually related problems

A circle with center in the first quadrant is tangent to y=x+10,y=x-6, and the y- axis.Let (h,k) be the center of the circle.If the value of (h+k)=a+b sqrt(a) where sqrt(a) is a surd,find the value of a+b

A circle with center in the first quadrant is tangent to y=x+10,y=x-6 and the Y-axis. Let (p,q) be the centre of the circle. If the value oif (p+q)=a+bsqrta when a, binQ , then the value of |a-b| is

The sides of a triangle ABC lie on the lines 3x+4y=0,4x+3y=0 and x=3. Let (h,k) be the centre of the circle inscribed in /_ABC. The value of (h+k) equals

In the following figure, O is the center of the circle. If x=40^(@) and x:y=4:3 , find the value of z.

The line 2x-y+1=0 is tangent to the circle at the point (2,5) and the center of the circle lies on x-2y=4. Then find the radius of the circle.

In the adjoining figure , O is the center of the circle. If angleBAD=30^(@) , then find the values of x,y and z.

Consider a circle with the X and Y axes as tangents to it in the first quadrant.If the line x+3y=8 passes through the center of the circle and the radius of the circle equals k, then find the value of 3k

A circle with centre at (15,-3) is tangent to y=(x^(2))/(3) at a point in the first quadrant.The radius of the circle is equal to

x ^(2) + hxy + y^(2) -6x -2y +k=0 is the equation of the circle and 2 is the radius of the circle, then find the values of h and k ?

MOTION-CIRCLE-Exercise - 3 (Subjective | JEE Advanced)
  1. Find the equation of the circle passing through the three points (4, 7...

    Text Solution

    |

  2. The line 2x - 3y +1=0 is tangent to a circle S=0 at (1, 1). If the r...

    Text Solution

    |

  3. A circle with center in the first quadrant is tangent to y = x+10, y =...

    Text Solution

    |

  4. A circle C is tangent to the x and y axis in the first quadrant at the...

    Text Solution

    |

  5. Tangents are drawn to the concentric circles x^2+y^2=a^2 and x^2 +y^2=...

    Text Solution

    |

  6. Find the locus of the mid point of the chord of a circle x^(2) + y^(2)...

    Text Solution

    |

  7. Find the equation of circle passing through (1, 1) belonging to the sy...

    Text Solution

    |

  8. A circle S = 0 is drawn with its centre at (-1, 1) so as to touch the ...

    Text Solution

    |

  9. Find the equation of the circle which passes through the point (1, 1) ...

    Text Solution

    |

  10. Find the equation of the circle whose radius is 3 and which touches ...

    Text Solution

    |

  11. Find the equation of the circle whose diameter is the common chord of ...

    Text Solution

    |

  12. If the radical axis of the circles x^2+y^2+2gx+2fy+c=0 and 2x^2+2y^2+3...

    Text Solution

    |

  13. Find the equation of the circle through the points of intersection of ...

    Text Solution

    |

  14. The centre of the circle S=0 lie on the line 2x – 2y +9=0 & S=0 cuts o...

    Text Solution

    |

  15. Find the equation of a circle passing through the origin if the line p...

    Text Solution

    |

  16. Find the equation of the circle which cuts the circle x^2 + y^2 - 14x...

    Text Solution

    |

  17. The locus of the centers of the circles which cut the circles x^(2) + ...

    Text Solution

    |

  18. The equation of a circle which touches the line x +y= 5 at N(-2,7) and...

    Text Solution

    |

  19. Find the equation of the circle passing through the point (– 6, 0) if ...

    Text Solution

    |

  20. Find the equation of the circle which passes through the origin, meets...

    Text Solution

    |