Home
Class 11
MATHS
If S(1)=alpha^(2)+beta^(2)-a^(2), then a...

If `S_(1)=alpha^(2)+beta^(2)-a^(2)`, then angle between the tangents from `(alpha, beta)` to the circle `x^(2)+y^(2)=a^(2)`, is

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|877 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE PUBLICATION|Exercise Multiple correct answers type|11 Videos

Similar Questions

Explore conceptually related problems

If the straight line y= x sin alpha + a sec alpha is a tangent to the circle x^(2) + y^(2) = a^(2) then-

If tan 2alpha = cot 2beta , then sec(alpha + beta) =

If alpha and beta are complementery angles, then the value of sec^2 alpha - cot^2 beta is

Suppose that the equation f(x)=x^(2)+bx+c=0 has two distinct real roots alpha and beta . The angle between the tangent to the curve y=f(x) at the point ((alpha+beta)/(2),f((alpha+beta)/(2))) and the positive direction of the x -axis is-

If (alpha +beta ) and (alpha - beta ) are the eccentric angles of the points P and Q respectively on the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 show that the equation of the chord PQ is (x)/(a) cos alpha+(y)/(b)sin alpha = cos beta .

If tan alpha =(1+2^(-x))^(-1) and tan beta =(1+2^(x+1))^(-1) then the value of (alpha + beta) is-

If alpha+ beta=(pi)/(2) and beta+ gamma= alpha then prove that tan alpha=tan beta+2 tan gamma .

Tangents drawn from the point (c, d) to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 make angles alpha and beta with the x-axis. If tan alpha tan beta=1 , then find the value of c^(2)-d^(2) .

If |alpha|,|beta| lt 1, s _(1) =1- alpha +alpha^(2) -alpha^(3)+…oo and s_(2)=1-beta +beta ^(2) -beta ^(3)+…oo then (1-alpha beta +alpha^(2) beta ^(2) -alpha ^(3) beta ^(3) +…oo) is equal to

The locus of a point P ( alpha , beta ) moving under the condition that the line y= alpha x + beta is a tangent to the hyperbola (x^(2))/(a^(2)) - (y^(2))/(b^(2))=1 is a/an-

CENGAGE PUBLICATION-CONIC SECTIONS-All Questions
  1. Prove that the equation of any tangent to the circle x^2+y^2-2x+4y-4=0...

    Text Solution

    |

  2. The tangent to the circle x^2+y^2=5 at (1,-2) also touches the circle ...

    Text Solution

    |

  3. If S(1)=alpha^(2)+beta^(2)-a^(2), then angle between the tangents from...

    Text Solution

    |

  4. If a >2b >0, then find the positive value of m for which y=m x-bsqrt(1...

    Text Solution

    |

  5. Find the angle between the two tangents from the origin to the circle ...

    Text Solution

    |

  6. Two circles C1 and C2 intersect at two distinct points PandQ in a line...

    Text Solution

    |

  7. Find the equation of the tangent at the endpoints of the diameter of ...

    Text Solution

    |

  8. Find the equations of the tangents to the circle x^2+y^2-6x+4y=12 whic...

    Text Solution

    |

  9. If from any point P on the circle x^2+y^2+2gx+2fy+c=0, tangents are dr...

    Text Solution

    |

  10. The lengths of the tangents from P(1,-1) and Q(3,3) to a circle are sq...

    Text Solution

    |

  11. Which of the following is a point on the common chord of the circle x^...

    Text Solution

    |

  12. If the circles x^2+y^2+2a x+c y+a=0 and x^2+y^2-3a x+d y-1=0 intersec...

    Text Solution

    |

  13. The circles x^2+y^2+x+y=0and x^2+y^2+x-y=0intersect at an angle of

    Text Solution

    |

  14. The common chord of x^2+y^2-4x-4y=0 and x^2+y^2=16 subtends at the ori...

    Text Solution

    |

  15. If the tangents are drawn to the circle x^2+y^2=12 at the point where ...

    Text Solution

    |

  16. If the circle x^2+y^2+2gx+2fy+c=0 bisects the circumference of the cir...

    Text Solution

    |

  17. Find the length of the common chord of the circles x^2+y^2+2x+6y=0 and...

    Text Solution

    |

  18. If the circle x^(2)+y^(2)=1 is completely contained in the circle x^(2...

    Text Solution

    |

  19. Prove that the pair of straight lines joining the origin to the points...

    Text Solution

    |

  20. The circles x^2+y^2-12 x-12 y=0 and x^2+y^2+6x+6y=0. a.touch each oth...

    Text Solution

    |