Home
Class 12
MATHS
The difference of the slopes of the line...

The difference of the slopes of the lines given by the equation `x^2(sec^2theta-sin^2theta)-2xytantheta+y^2sin^2theta=0` is.

A

`sin 2 theta`

B

`cos 2theta`

C

`1`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
D
Let the two lines represented by given equation are `y=m_(1)x` and `y=m_(2)x`
`therefore m_(1)+m_(2)=2 sec thetacosectheta and m_(1)m_(2)=sec^2 theta cosec^(2)theta-1`
Also , `(m_1-m_2)^2=(m_1+m+2)^2-4m_1m_2`
`rArr m_1-m_2=2`
Promotional Banner

Topper's Solved these Questions

  • PRACTICE SET 01

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Paper 2 (Mathematics)|50 Videos

  • PRACTICE SET 03

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise PAPER 2 (MATHEMATICS)|49 Videos

Similar Questions

Explore conceptually related problems

Difference of slopes of the lines represented by the equation x^(2)(sec^(2)theta-sin^(2)theta)-2xy tan theta+y^(2)sin^(2)theta=0 is (A) 4 (B) 3 (C) 2 (D) None of these

The difference of the slopes of the lines represented by x^(2)(sec^(2)theta-sin^(2)theta)-(2tan theta)xy+y^(2)sin^(2)theta=0

The difference of the tangents of the angles which the lines x^(2)(sec^(2)-sin^(2)theta)-2xy tan theta +y^(2)sin^(2) theta=0 make with X-axis, is

Solve the equation 3-2cos theta-4sin theta-cos2 theta+sin2 theta=0

tan^(2)theta-sin^(2)theta=sin^(4)theta sec^(2)theta

(sec^2 theta-1)/(sec^2 theta)- sin^2 theta=

(sec theta-tan theta)^2 (1+sin theta)^2 div sin^2 theta

Prove that cosec^2theta+sec^2theta=(sec^2theta)/(sin^2theta)

If sec^4theta+sec^2theta=10+tan^4theta+tan^2theta", then "sin^2theta=

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 02-Paper 2 (Mathematics )
  1. int cos (loge x)dx is equal to

    Text Solution

    |

  2. The switching function ffor switching network is

    Text Solution

    |

  3. The difference of the slopes of the lines given by the equation x^2(se...

    Text Solution

    |

  4. Let p ^^ (q vv r)=(p ^^ q) vv(p ^^ r). Then this law is known as

    Text Solution

    |

  5. If |a|=|b|=1 and |a+b|=sqrt(3), then the value of (3a-4b)(2b+5b) is

    Text Solution

    |

  6. A particle moves in a straight line so that s=sqrt(t), then its accele...

    Text Solution

    |

  7. Le t f(x) ={{:((sinpix)/(5x)",",xne0),(" "k",",x=0):} if (x) is contin...

    Text Solution

    |

  8. lim(xto0)(loge(1+x))/(3^x-1) is equal to

    Text Solution

    |

  9. The differential equation for which sin^(-1) x + sin^(-1) y = c is giv...

    Text Solution

    |

  10. The probability that in a family of 5 members,exactly two members have...

    Text Solution

    |

  11. The solution of y'-y = 1 , y(0)=-1 is given by y(x) =

    Text Solution

    |

  12. There is a group of 265 persons who like either singing or dancing or ...

    Text Solution

    |

  13. Let R be a relation on N defined by R = {(x, y): 2x + y = 10}, then do...

    Text Solution

    |

  14. The period of sin^2theta is

    Text Solution

    |

  15. Six numbers are in AP such that their sum is 3 . The first term is 4 ...

    Text Solution

    |

  16. The value of k such that the lines 2x-3y+k=0,3x-4y-13=0 and 8x-11y-33=...

    Text Solution

    |

  17. If one end of a diameter of the circle x^(2)+y^(2)-4x-6y+11=0 is (3, ...

    Text Solution

    |

  18. A man and his wife appear for an interview for two posts. The probabil...

    Text Solution

    |

  19. The area bounded by the curve x=3y^2-9 and the line x=0,y=0 and y=1 is

    Text Solution

    |

  20. The vector hat(i)+xhat(j)+3hat(k) is rotated through an angle theta an...

    Text Solution

    |