Home
Class 11
MATHS
Tangents are drawn to the ellipse (x^2)/...

Tangents are drawn to the ellipse `(x^2)/(a^2)+(y^2)/(b^2)=1,(a > b),` and the circle `x^2+y^2=a^2` at the points where a common ordinate cuts them (on the same side of the x-axis). Then the greatest acute angle between these tangents is given by (A) `tan^(-1)((a-b)/(2sqrt(a b)))` (B) `tan^(-1)((a+b)/(2sqrt(a b)))` (C) `tan^(-1)((2a b)/(sqrt(a-b)))` (D) `tan^(-1)((2a b)/(sqrt(a+b)))`

Text Solution

AI Generated Solution

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

A normal to parabola, whose inclination is 30^(@) , cuts it again at an angle of (a) tan^(-1)((sqrt(3))/(2)) (b) tan^(-1)((2)/(sqrt(3))) (c) tan^(-1)(2sqrt(3)) (d) tan^(-1)((1)/(2sqrt(3)))

Prove that the ellipse x^2/a^2 + y^2/b^2 = 1 and the circle x^2 + y^2 = ab intersect at an angle tan^(-1) (|a-b|/sqrt(ab)) .

Tangents are drawn to the ellipse from the point ((a^2)/(sqrt(a^2-b^2)),sqrt(a^2+b^2))) . Prove that the tangents intercept on the ordinate through the nearer focus a distance equal to the major axis.

A tangent is drawn to the ellipse to cut the ellipse x^2/a^2+y^2/b^2=1 and to cut the ellipse x^2/c^2+y^2/d^2=1 at the points P and Q. If the tangents are at right angles, then the value of (a^2/c^2)+(b^2/d^2) is

The slopes of the common tangents of the ellipse (x^2)/4+(y^2)/1=1 and the circle x^2+y^2=3 are +-1 (b) +-sqrt(2) (c) +-sqrt(3) (d) none of these

Let a, b and c be positive real numbers. Then prove that tan^(-1) sqrt((a(a + b + c))/(bc)) + tan^(-1) sqrt((b (a + b + c))/(ca)) + tan^(-1) sqrt((c(a + b+ c))/(ab)) =' pi'

If a , b , c >0 and s=(a+b+c)/2,p rov et h a t tan^(-1)sqrt((2a s)/(b c))+tan^(-1)sqrt((2b s)/(c a))+tan^(-1)sqrt((2c s)/(a b))=pi

The angle between the lines joining origin to the points of intersection of the line sqrt(3)x+y=2 and the curve y^2-x^2=4 is (A) tan^(-1)(2/(sqrt(3))) (B) pi/6 (C) tan^(-1)((sqrt(3))/2) (D) pi/2

If the ellipse x^2/a^2+y^2/b^2=1 (b > a) and the parabola y^2 = 4ax cut at right angles, then eccentricity of the ellipse is (a) (3)/(5) (b) (2)/(3) (c) (1)/(sqrt(2)) (d) (1)/(2)

If a , b , c >0 and s=(a+b+c)/2 , prove that tan^(-1)sqrt((2a s)/(b c))+tan^(-1)sqrt((2b s)/(c a))+tan^(-1)sqrt((2c s)/(a b))=pi

CENGAGE ENGLISH-CONIC SECTIONS-All Questions
  1. If any line perpendicular to the transverse axis cuts the hyperbola (x...

    Text Solution

    |

  2. If the focal distance of an end of the minor axis of an ellipse (ref...

    Text Solution

    |

  3. Tangents are drawn to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1,(a > b), ...

    Text Solution

    |

  4. A normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 meets the ...

    Text Solution

    |

  5. Find the eccentricity of an ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 ...

    Text Solution

    |

  6. The slopes of the common tangents of the ellipse (x^2)/4+(y^2)/1=1 and...

    Text Solution

    |

  7. Find the locus of the midpoints of chords of hyperbola 3x^(2)-2y^(2)+4...

    Text Solution

    |

  8. The coordinates of the vertices Ba n dC of a triangle A B C are (2,...

    Text Solution

    |

  9. If the tangents to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 make angles a...

    Text Solution

    |

  10. If P=(x , y),F1=(3,0),F2=(-3,0), and 16 x^2+25 y^2=400 , then P F1+P F...

    Text Solution

    |

  11. Find the condition on a and b for which two distinct chords of the hyp...

    Text Solution

    |

  12. The point of intersection of the tangents at the point P on the ellip...

    Text Solution

    |

  13. Find the equation of the ellipse (referred to its axes as the axes o...

    Text Solution

    |

  14. Tangents are drawn to the ellipse x^2/a^2+y^2/b^2=1 at two points who...

    Text Solution

    |

  15. The sum of the squares of the perpendiculars on any tangents to the ...

    Text Solution

    |

  16. A rod of length 12 cm moves with its ends always touching the coord...

    Text Solution

    |

  17. Tangents are drawn from the points on the line x−y−5=0 to x^2+4y^2=4, ...

    Text Solution

    |

  18. If alpha-beta= constant, then the locus of the point of intersection o...

    Text Solution

    |

  19. Two circles are given such that one is completely lying inside the ...

    Text Solution

    |

  20. How many real tangents can be drawn from the point (4, 3) to the hy...

    Text Solution

    |