Home
Class 12
MATHS
The locus of the point x=a cos theta, y=...

The locus of the point `x=a cos theta, y=b sin theta` is

A

`(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`

B

`(x^(2))/(a^(2))+(y^(2))/(b^(2))=1`

C

`(x^(2))/(a^(2))+(y^(2))/(b^(2))=2`

D

`a^(2) x^(2)+b^(2) y^(2)=1`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|306 Videos

  • Definite Integrals and its Application

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|453 Videos

Similar Questions

Explore conceptually related problems

The locus of the point x=a+b cos theta y=b+a sin theta is

The locus of the point x=a+sec theta y=b+a tan theta is

The locus of the point x=a(cos theta+sin theta) y=b (cos theta-sin theta) is

The locus of the point (a cos ^(3) theta, a sin ^(3) theta) is

The length of the chord joining the points (4 cos theta , 4 sin theta ) and (4 cos ( theta+ 60^@ ), 4 sin ( theta+ 60^@ )) of the circle x^2+y^2=16 is :

The length of the chord joining the points (4 cos theta, 4 sin theta) and (4 cos (theta+60^(2)),4 sin (theta+60^(@))) of the circle x^(2)+y^(2)=16 is

The locus of the point of intersection of tangents to the circles x=a cos theta, y = a sin theta at points whose parametric angle differs by pi//4 is

The distance between the points (a cos theta, a sin theta) and (a cos varphi, a sin varphi) is 2 a , then theta=

Prove that the product of the lengths of the perpendiculars drawn from the points (sqrt(a^(2) - b^(2)) , 0) " and " (- sqrt(a^(2) - b^(2)), 0) to the line x/a cos theta + y/b sin theta = 1 " is " b^(2) .

HIMALAYA PUBLICATION-COORDINATE SYSTEMS, LOCUS AND STRAIGHT LINES-QUESTION BANK
  1. A straight rod of length 9 units slides with its ends A, B always on t...

    Text Solution

    |

  2. The locus of the mid-point of the portion of the line xcos alpha+y sin...

    Text Solution

    |

  3. The locus of the point x=a cos theta, y=b sin theta is

    Text Solution

    |

  4. The locus of the point x=a(cos theta+sin theta) <bx> y=b (cos theta-si...

    Text Solution

    |

  5. The locus of the point x=a+b cos theta y=b+a sin theta is

    Text Solution

    |

  6. The locus of the point x=a+sec theta y=b+a tan theta is

    Text Solution

    |

  7. The locus of the point (a cos ^(3) theta, a sin ^(3) theta) is

    Text Solution

    |

  8. The locus of the point (a+b t, b-(a)/(t)), where t is the parameter is

    Text Solution

    |

  9. A line segment A B of length ' a ' moves with its ends on the axes. Th...

    Text Solution

    |

  10. Distance between the parallel lines 3 x+4 y+7=0 and 6 x+8 y+k=0 is 4 ....

    Text Solution

    |

  11. Equation of the line cutting off an intercept 2 from the negative dire...

    Text Solution

    |

  12. Equation of the line perpendicular to y=x and passing through (3,2) is

    Text Solution

    |

  13. The length of the perpendicular from the point (a cos alpha, a sin alp...

    Text Solution

    |

  14. If the quadrilateral formed by the lines a x+b y+c=0, a^(prime) x...

    Text Solution

    |

  15. If the algebraic sum of the perpendicular distances from the points (2...

    Text Solution

    |

  16. A point moves in the x y -plane such that the sum of its distances fro...

    Text Solution

    |

  17. The incentre of the triangle formed by the axes and the line (x)/(4)+(...

    Text Solution

    |

  18. The incentre of the triangle formed by (x)/(a)+(y)/(b)=1 is

    Text Solution

    |

  19. If the line segment joining (2,3) and (-1,2) is divided internally in ...

    Text Solution

    |

  20. If A=(6,3), B=(-3,5), C=(4,-2) and D=(x, 3 x) are four points, if [ar(...

    Text Solution

    |