Home
Class 12
MATHS
If (alpha,beta) is a point on the circle...

If `(alpha,beta)` is a point on the circle whose center is on the x-axis and which touches the line `x+y=0` at `(2,-2),` then the greatest value of `alpha` is `4-sqrt(2)` (b) 6 `4+2sqrt(2)` (d) `+sqrt(2)`

A

`4-sqrt(2)`

B

6

C

`4+2sqrt(2)`

D

`4+sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
3
If (a,0) is the center C and P is P is (2,-2) , then `/_ COP =45^(@)`.

Since the equation of OP is `x+y=0`, we have
`OP =2sqrt(2)=CP`
Hence, `OC=4`.
The point on the circle with the greatest x coordinate is B.
`alpha = OP=OC+CB=4+2sqrt(2)`
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

If (alpha ,beta) is a point on the circle whose centre is on the x-axis and which touches the line x+y=0 at (2,-2), then the greatest value of 'alpha' is :

If (alpha,beta) is a point on the circle whose center is on the x-axis and which touches the line x+y=0 at (2,-2), then the greatest value of alpha is (a) 4-sqrt(2) (b) 6 (c) 4+2sqrt(2) (d) +sqrt(2)

If the point P(a ,a^2) lies completely inside the triangle formed by the lines x=0,y=0, and x+y=2, then find the exhaustive range of values of a is (A) (0,1) (B) (1,sqrt2) (C) (sqrt2 -1,1) (D) (sqrt2 -1,2)

If alpha,a n dbeta be the roots of the equation x^2+p x-1//2p^2=0,w h e r ep in Rdot Then the minimum value of alpha^4+beta^4 is 2sqrt(2) b. 2-sqrt(2) c. 2 d. 2+sqrt(2)

Prove that the greatest value of x y is c^3/sqrt(2a b) , if a^2x^4+b^2y^4=c^6dot

The equation of a circle is x^2+y^2=4. Find the center of the smallest circle touching the circle and the line x+y=5sqrt(2)

The equation of the line that touches the curves y=x|x| and x^2+(y-2)^2=4 , where x!=0, is: (a)y=4 sqrt(5) x +20 (b)y=4 sqrt(3) x -12 (c)y=0 (d) y=-4 sqrt(5) x -20

The point on the parabola y^(2) = 8x at which the normal is inclined at 60^(@) to the x-axis has the co-ordinates as (a) (6,-4sqrt(3)) (b) (6,4sqrt(3)) (c) (-6,-4sqrt(3)) (d) (-6,4sqrt(3))

A parabola y=a x^2+b x+c crosses the x-axis at (alpha,0)(beta,0) both to the right of the origin. A circle also passes through these two points. The length of a tangent from the origin to the circle is: (a) sqrt((b c)/a) (b) a c^2 (c) b/a (d) sqrt(c/a)

The coordinates of a point on the line x + y + 1 = 0 which is at a distance sqrt(2) units from the line 3x + 4y - 2 = 0 are

CENGAGE PUBLICATION-CIRCLE -Excercises (Single Correct Answer Type)
  1. If a line passes through the point P(1,-2) and cuts the x^2+y^2-x-y= 0...

    Text Solution

    |

  2. The area of the triangle formed by joining the origin to the point of ...

    Text Solution

    |

  3. If (alpha,beta) is a point on the circle whose center is on the x-axis...

    Text Solution

    |

  4. The area bounded by the circles x^2+y^2=1,x^2+y^2=4, and the pair of l...

    Text Solution

    |

  5. The number of intergral value of y for which the chord of the circle x...

    Text Solution

    |

  6. The straight line xcostheta+ysintheta=2 will touch the circle x^2+y^2-...

    Text Solution

    |

  7. The range of values of lambda,(lambda>0) such that the angle theta bet...

    Text Solution

    |

  8. The circle which can be drawn to pass through (1, 0) and (3, 0) and to...

    Text Solution

    |

  9. The locus of the midpoints of the chords of contact of x^2+y^2=2 from ...

    Text Solution

    |

  10. If a circle of radius r is touching the lines x^2-4x y+y^2=0 in the fi...

    Text Solution

    |

  11. The locus of the midpoints of the chords of the circle x^2+y^2-a x-b y...

    Text Solution

    |

  12. Any circle through the point of intersection of the lines x+sqrt(3)y=1...

    Text Solution

    |

  13. If the pair of straight lines x ysqrt(3)-x^2=0 is tangent to the circl...

    Text Solution

    |

  14. The condition that the chord xcosalpha+ysinalpha-p=0 of x^2+y^2-a^2=0 ...

    Text Solution

    |

  15. The centres of a set of circles, each of radius 3, lie on the circle x...

    Text Solution

    |

  16. The equation of the locus of the middle point of a chord of the circle...

    Text Solution

    |

  17. The angle between the pair of tangents drawn from a point P to the cir...

    Text Solution

    |

  18. If two distinct chords, drawn from the point (p, q) on the circle x^2+...

    Text Solution

    |

  19. about to only mathematics

    Text Solution

    |

  20. Through the point P(3,4) a pair of perpendicular lines are drawn which...

    Text Solution

    |