Home
Class 12
MATHS
Radius of the circle that passes through...

Radius of the circle that passes through the origin and touches the parabola `y^2=4a x` at the point `(a ,2a)` is

A

`(5)/(sqrt(2))a`

B

`2sqrt(2)a`

C

`sqrt((5)/(2)a`

D

`(3)/(sqrt(2))a`

Text Solution

Verified by Experts

The correct Answer is:
A
(1)
The equation of tangent to the parabola at (a,2a) is
2ya=2a(x+a)
or y-x-a=0
The passes through (0,0). Therefore,
`a^(2)+4a^(2)+lamda(-a)=0orlamda=5a`
Thus, the required circle is `x^(2)+y^(2)-7ax-ay=0`.
Its radius is
`sqrt((49)/(4)a^(2)+(a^(2))/(4))=(5)/(sqrt(2))a`
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE PUBLICATION|Exercise EXERCISE (MULTIPLE CORRECT ANSWER TYPE )|26 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise LINKED COMPREHENSION TYPE|45 Videos

  • PARABOLA

    CENGAGE PUBLICATION|Exercise Concept Applications Exercise 5.7|9 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise Numberical Value Type|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE PUBLICATION|Exercise Comprehension|8 Videos

Similar Questions

Explore conceptually related problems

Find the equation of the circle, passing through the origin and the foci of the parabolas y^(2) = 8x and x^(2) = 24 y .

Find the radius of the largest circle, which passes through the focus of the parabola y^2=4(x+y) and is also contained in it.

The common chord of the circle x^2+y^2+6x+8y-7=0 and a circle passing through the origin and touching the line y=x always passes through the point. (a) (-1/2,1/2) (b) (1, 1) (c) (1/2,1/2) (d) none of these

A circle passes through the point (-2, 1) and touches the straight line 3x - 2y = 6 at the point (4, 3) . Find its equation.

Find the circle of minimum radius which passes through the point (4, 3) and touches the circle x^2+y^2=4 externally.

If a line passing through the origin touches the circle (x-4)^2+(y+5)^2=25 , then find its slope.

Find the locus of the midpoint of chords of the parabola y^2=4a x that pass through the point (3a ,a)dot

Find the equation of the circles which passes through the origin and the points of intersection of the circles x^(2) + y^(2) - 4x - 8y + 16 = 0 and x^(2) + y^(2) + 6x - 4y - 3 = 0 .

If r_1 and r_2 are the radii of smallest and largest circles which passes through (5,6) and touches the circle (x-2)^2+y^2=4 , then r_1,r_2 is

Let be the circle with centre at (1 , 1) and radius is 1 unit . It T is the circle centred at (0 , y) , passing through origin and touching the circle c externally , then the radius of T is equal to _

CENGAGE PUBLICATION-PARABOLA-EXERCISE (SINGLE CORRECT ANSWER TYPE )
  1. Show that the tangents to the curve y=x^2-5x+6 at the point (2,0) and ...

    Text Solution

    |

  2. Two mutually perpendicular tangents of the parabola y^(2)=4ax meet the...

    Text Solution

    |

  3. Radius of the circle that passes through the origin and touches the ...

    Text Solution

    |

  4. The mirror image of the parabola y^2= 4x in the tangent to the parabol...

    Text Solution

    |

  5. Consider the parabola y^2=4xdot Let A-=(4,-4) and B-=(9,6) be two fixe...

    Text Solution

    |

  6. A line of slope lambda(0 < lambda < 1) touches the parabola y+3x^2=0 a...

    Text Solution

    |

  7. The tangent at any point P onthe parabola y^2=4a x intersects the y-ax...

    Text Solution

    |

  8. If P(t^2,2t),t in [0,2] , is an arbitrary point on the parabola y^2=4x...

    Text Solution

    |

  9. The minimum area of circle which touches the parabolas y=x^2+1 and y^2...

    Text Solution

    |

  10. If the tangents and normals at the extremities of a focal chord of a ...

    Text Solution

    |

  11. At what point on the parabola y^2=4x the normal makes equal angle with...

    Text Solution

    |

  12. The line 2x+y+lamda=0 is a normal to the parabola y^(2)=8x, is lamda=

    Text Solution

    |

  13. about to only mathematics

    Text Solution

    |

  14. The equation of the line that passes through (10 ,-1) and is perpendic...

    Text Solution

    |

  15. Tangent and normal drawn to a parabola at A(a t^2,2a t),t!=0 meet the ...

    Text Solution

    |

  16. The radius of the circle touching the parabola y^2=x at (1, 1) and hav...

    Text Solution

    |

  17. If two different tangents of y^2=4x are the normals to x^2=4b y , then

    Text Solution

    |

  18. The equation of the common tangent to the parabolas y^2= 4ax and x^2=...

    Text Solution

    |

  19. If line P Q , where equation is y=2x+k , is a normal to the parabola w...

    Text Solution

    |

  20. Evaluate, min[(x1-x2)^2+(5+sqrt(1-x1^2)-sqrt(4x2))^2],AAx1,x2 in R , ...

    Text Solution

    |