Home
Class 11
MATHS
Tangent is drawn at any point (x1, y1) o...

Tangent is drawn at any point `(x_1, y_1)` other than the vertex on the parabola `y^2=4a x` . If tangents are drawn from any point on this tangent to the circle `x^2+y^2=a^2` such that all the chords of contact pass through a fixed point `(x_2,y_2),` then (a) `x_1, a ,x_2` in GP (b) `(y_1)/2,a ,y_2` are in GP
(c)`-4,(y_1)/(y_2),x_1/x_2` are in GP (d) `x_1x_2+y_1y_2=a^2`

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE ENGLISH|Exercise All Questions|886 Videos
  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

Tangent is drawn at any point (x_1,y_1) on the parabola y^2=4ax . Now tangents are drawn from any point on this tangent to the circle x^2+y^2=a^2 such that all the chords of contact pass throught a fixed point (x_2,y_2) Prove that 4(x_1/x_2)+(y_1/y_2)^2=0 .

From a variable point p on line 2x−y-1=0 pair of tangents are drawn to parabola x^2=8y then chord of contact passes through a fixed point.

From a point on the line y=x+c , c(parameter), tangents are drawn to the hyperbola (x^(2))/(2)-(y^(2))/(1)=1 such that chords of contact pass through a fixed point (x_1, y_1) . Then , (x_1)/(y_1) is equal to

Tangents are drawn to x^(2)+y^(2)=1 from any arbitrary point P on the line 2x+y-4=0 .Prove that corresponding chords of contact pass through a fixed point and find that point.

The chords of contact of the pair of tangents drawn from each point on the line 2x + y=4 to the circle x^2 + y^2=1 pass through the point (h,k) then 4(h+k) is

Tangents drawn from a point on the circle x^2+y^2=9 to the hyperbola x^2/25-y^2/16=1, then tangents are at angle

From a point on the line x-y+2=0 tangents are drawn to the hyperbola (x^(2))/(6)-(y^(2))/(2)=1 such that the chord of contact passes through a fixed point (lambda, mu) . Then, mu-lambda is equal to

Tangents are drawn from any point on the hyperbola (x^2)/9-(y^2)/4=1 to the circle x^2+y^2=9 . Find the locus of the midpoint of the chord of contact.

Tangents are drawn from a point on the ellipse x^2/a^2 + y^2/b^2 = 1 on the circle x^2 + y^2 = r^2 . Prove that the chord of contact are tangents of the ellipse a^2 x^2 + b^2 y^2 = r^4 .

The length of the chord of contact of the tangents drawn from the point (-2,3) to the circle x^2+y^2-4x-6y+12=0 is:

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. Tangent is drawn at any point (p ,q) on the parabola y^2=4a x .Tangent...

    Text Solution

    |

  2. The equation of the directrix of the parabola with vertex at the origi...

    Text Solution

    |

  3. Tangent is drawn at any point (x1, y1) other than the vertex on the pa...

    Text Solution

    |

  4. The angle between the tangents to the curve y=x^2-5x+6 at the point (2...

    Text Solution

    |

  5. Statement 1: If the parabola y^2=4a x and the circle x^2+y^2+2b x=0 to...

    Text Solution

    |

  6. If a line y=3x+1 cuts the parabola x^2-4x-4y+20=0 at A and B , then th...

    Text Solution

    |

  7. P(x , y) is a variable point on the parabola y^2=4a x and Q(x+c ,y+c) ...

    Text Solution

    |

  8. If a and c are the lengths of segments of any focal chord of the parab...

    Text Solution

    |

  9. AB is a chord of the parabola y^2 = 4ax with its vertex at A. BC is dr...

    Text Solution

    |

  10. The set of values of alpha for which the point (alpha,1) lies inside t...

    Text Solution

    |

  11. If P be a point on the parabola y^2=3(2x-3) and M is the foot of perpe...

    Text Solution

    |

  12. If y=m x+c touches the parabola y^2=4a(x+a), then (a)c=a/m (b) c=a m...

    Text Solution

    |

  13. The angle between the tangents to the parabola y^2=4a x at the points ...

    Text Solution

    |

  14. The area of the triangle formed by the tangent and the normal to the ...

    Text Solution

    |

  15. Double ordinate A B of the parabola y^2=4a x subtends an angle pi/2 at...

    Text Solution

    |

  16. Statement 1: The normals at the points (4, 4) and (1/4,-1) of the para...

    Text Solution

    |

  17. The tangent PT and the normal PN to the parabola y^2=4ax at a point P...

    Text Solution

    |

  18. Let A and B be two distinct points on the parabola y^2=4x. If the ax...

    Text Solution

    |

  19. The equations of the common tangents to the parabola y = x^2 and y=-...

    Text Solution

    |

  20. about to only mathematics

    Text Solution

    |