Home
Class 12
MATHS
If A B is a focal chord of x^2-2x+y-2=0 ...

If `A B` is a focal chord of `x^2-2x+y-2=0` whose focus is `S` and `A S=l_1,` then find `B Sdot`

Text Solution

Verified by Experts

`x^(2)-2x+y-2=0`
`orx^(2)-2x+1=3-y`
`or(x-1)^(2)=-(y-3)`
The length of its latus rectum is 1 unit.
Since AS, 1/2, and BS are in HP, we have
`(1)/(2)=(2ASxxBS)/(AS+BS)`
`or" "BS=(l_(1))/((4l_(1)-1))`
Promotional Banner

Topper's Solved these Questions

  • PARABOLA

    CENGAGE|Exercise Exercise 5.1|11 Videos

  • PARABOLA

    CENGAGE|Exercise Exercise 5.2|17 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE|Exercise Exercise (Numerical)|5 Videos

  • PERMUTATION AND COMBINATION

    CENGAGE|Exercise Question Bank|19 Videos

Similar Questions

Explore conceptually related problems

If AB is a focal chord of x^(2)-2x+y-2=0 whose focus is S and AS=l_(1), then find BS .

Consider a parabla y^(2)=8x . If PSQ is a focal chord of the parabola whose vertex is A and focus S,V being the middle point of the chord such that PV^(2)=AV^(2)+lamda.AS^(2) where lamda is______

If PSQ is a focal chord of a parabola y^(2)=6x , where S is the focus.Then the minimum value of PS.QS is

If PQ is a focal chord of the parabola y^(2)=4ax with focus at s, then (2SP.SQ)/(SP+SQ)=

If AB is a focal chord of the parabola y^(2)=4ax whose vertex is 0, then(slope of OA ) x (slope of OB)-

If (2,-8) is at an end of a focal chord of the parabola y^(2)=32x, then find the other end of the chord.

If PSQ is focal chord of parabola y^(2)=4ax(a>0), where S is focus then prove that (1)/(PS)+(1)/(SQ)=(1)/(a)

The focal chord of the parabola y^(2)=ax is 2x-y-8=0. Then find the equation of the directrix.

A straight line PQ touches the ellipse x^(2)/a^(2)+y^(2)/b^(2)=1 and the circle x^(2)+y^(2)=r^(2)(bltrlta) . RS is a focal chord of the ellipse. If RS is parallel to PQ and meets the circle at points R and S. Find the length of RS.

PSQ is a focal chord of the ellipse 4x^(2)+9y^(2)=36 such that SP=4. If S the another focus write the value of SQ.

CENGAGE-PARABOLA-Question Bank
  1. If A B is a focal chord of x^2-2x+y-2=0 whose focus is S and A S=l1, t...

    Text Solution

    |

  2. If (alpha, beta) is a point on parabola y^2=4 x which is nearest to th...

    Text Solution

    |

  3. The, focall chord of the parabola (y-2)^2=16(x-1) is a tangent to the ...

    Text Solution

    |

  4. A chord P Q is a normal to the y^2=4 a x at P and subtendsa right ang...

    Text Solution

    |

  5. If radius of circle passing through the focus of parabola x^2=4 y and ...

    Text Solution

    |

  6. The equation of latus rectum of a parabola is x+y=8 and cquation of th...

    Text Solution

    |

  7. Normals of parabola y^2=4 x at P and Q meet at R(x2, 0) and tangents a...

    Text Solution

    |

  8. Chord of the curve 3 x^2-y^2-2 x+4 y=0, which subtends a right angle a...

    Text Solution

    |

  9. If the equation lambda(4 x-3)^2+4(2 y-7)^2right=mu(4 x-3 y+3)^2 repres...

    Text Solution

    |

  10. Tangents are drawn from any point.on directrix of y^2=16 x to parabola...

    Text Solution

    |

  11. Absoulte value of y -intercept of the common tangent to the parabola y...

    Text Solution

    |

  12. Let y=x+1 be the axis of parabola, y+x-4=0 be the tangent of same para...

    Text Solution

    |

  13. Let the parabola y=a x^2+b x+c has vertex at M(4,2) and a in[1,3] . If...

    Text Solution

    |

  14. From the point (4,6), a pair of tangent lines is drawn to the parabola...

    Text Solution

    |

  15. If the normal to a parabola y^2=4 a x at P meets the curve again in Q ...

    Text Solution

    |

  16. A circle is drawn to pass through the extremities of the latus rectum ...

    Text Solution

    |

  17. If (-2,7) is the highest point on the graph of y=-2 x^2-4 a x+k, ...

    Text Solution

    |

  18. The tangent at P(1,2) to the parabola y^2=4 x meets the tangent at ver...

    Text Solution

    |

  19. If three normals are drawn from the point (6,0) to the parabola y^2=4 ...

    Text Solution

    |

  20. Square of the area of the triangle formed by end points of a focal cho...

    Text Solution

    |

  21. Let S be the set all points (x, y) satisfying y^2 le 16 x . For points...

    Text Solution

    |