Home
Class 12
MATHS
Let a & b be any two numbers satisfying ...

Let a & b be any two numbers satisfying `1/a^2 + 1/b^2 = 1/4`.Then, the foot of the perpendicular from the origin on variable line `x/a + y/b = 1` lies on

A

a hyperbola with each semi-axis = `sqrt2`

B

a hyperbola with each semi-axis = 2

C

a circle of radius = 2

D

a circle of radius = `sqrt2`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    DISHA PUBLICATION|Exercise Exercise : -1 Concept Builder (Topicwise -1)|9 Videos
  • CONIC SECTIONS

    DISHA PUBLICATION|Exercise Exercise : -1 Concept Builder (Topicwise -2)|7 Videos
  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    DISHA PUBLICATION|Exercise Exercise -2 : Concept Applicator|30 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    DISHA PUBLICATION|Exercise Exercise-2 : Concept Applicator|30 Videos

Similar Questions

Explore conceptually related problems

Let a o* b be any two numbers satisfying (1)/(a^(2))+(1)/(b^(2))=(1)/(4) .Then,the foot of the perpendicular from the origin on variable line (x)/(a)+(y)/(b)=1 lies on

The length of perpendicular from the origin on the line x/a + y/b = 1 is -

The locus of the foot of the perpendicular from the foci an any tangent to the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 , is

Co - ordinates of the foot of the perpendicular drawn from the origin to the plane 2x+3y-4z + 1 = 0 are

A variable line cuts pair of lines x^(2)-(a+b)x+ab=0 in such a way that intercept between subtends a right angle at origin.The locus of the foot of the perpendicular from origin on variable line is

Find the coordinates of the foot of the perpendicular drawn from the point (1,-2) on the line y=2x+1

The locus of the foot of the perpendicular from the origin on each member of the family (4a+3)x-(a+1)y-(2a+1)=0

DISHA PUBLICATION-CONIC SECTIONS-Exercise-2 : Concept Applicator
  1. Let a & b be any two numbers satisfying 1/a^2 + 1/b^2 = 1/4.Then, the ...

    Text Solution

    |

  2. A circle C1, of radius 2 touches both x-axis and y- axis. Another circ...

    Text Solution

    |

  3. The equation of tangents drawn from the origin to the circlex^2+y^2-2r...

    Text Solution

    |

  4. Let AB be a chord of the circle x^(2) +y^(2) =r^(2) subtending a right...

    Text Solution

    |

  5. The line joining (5,0) to (10cos theta,10sin theta) is divided interna...

    Text Solution

    |

  6. Four distinct points (2k,3k) , (1,0), (0,1) and (0,0) lies on a circl...

    Text Solution

    |

  7. The number of integral values of lambda for which the equation x^2+y^2...

    Text Solution

    |

  8. The cable of a uniformly loaded suspension bridge hangs in the form...

    Text Solution

    |

  9. If from any point P, tangents PT, PT' are drawn to two given circles w...

    Text Solution

    |

  10. y=2x is a chord of the circle x^2 + y^2-10x = 0, then the equation of ...

    Text Solution

    |

  11. If a!=0 and the line 2bx+3cy+4d=0 passes through the points of interse...

    Text Solution

    |

  12. Q57) If the circle x^2+y^2+2ax+cy+a=0 and x^2+y^2-3ax+dy-1=0 intersect...

    Text Solution

    |

  13. A rod AB of length 15 cm rests in between two coordinate axes in su...

    Text Solution

    |

  14. Find the area of the triangle formed by the lines joining the vertex o...

    Text Solution

    |

  15. The eccentricities of the ellipse x^(2)/alpha^(2)+y^(2)/beta^(2)=1,alp...

    Text Solution

    |

  16. The middle point of chord x+3y=2 of the conic x^(2)+xy-y^(2)=1, is

    Text Solution

    |

  17. If x^2/a^2+y^2/b^2=1(a>b) and x^2-y^2=c^2 cut at right angles, then:

    Text Solution

    |

  18. If the line x+my+am^(2)=0 touches the parabola y^(2)= 4ax then the pon...

    Text Solution

    |

  19. The equation of the conic with focus at (1,-1), directrix along x -y +...

    Text Solution

    |

  20. The equation of one of the common tangent to the parabola y^(2) = 8x a...

    Text Solution

    |

  21. If two circles (x-1)^(2)+(y-3)^(2)=r^(2) and x^(2)+y^(2)-8x+2y+8=0 int...

    Text Solution

    |