Home
Class 12
MATHS
Show that the quadrilateral formed by th...

Show that the quadrilateral formed by the four lines `y=mx+a sqrt(a+m^(2)),x+a sqrt(1+m^(2)), y= mx-a sqrt(1+m^(2)) and y= mx-a sqrt(1+m^(2))` is a square of rhombus accroding as `mm=- or m m ne -1`

Promotional Banner

Topper's Solved these Questions

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise COORDINATE GEOMETRY (THREE DIMENSIONAL COORDINATE GEOMETRY)|10 Videos

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise CALCULUS|84 Videos

  • MISCELLANEOUS EXAMPLES

    CHHAYA PUBLICATION|Exercise ALGEBRA|141 Videos

  • METHOD OF SUBSTITUTION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Assertion-Reason Type)|2 Videos

  • ORDER AND DEGREE OF DIFFERENTIAL EQUATION

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (E Assertion - Reasion Type )|2 Videos

Similar Questions

Explore conceptually related problems

Show that the area of the triangle formed by the lines y = m_(1) x + c_(1) , y = m_(2) x + c_(2) " and " x = 0 " is " ((c_(1) - c_(2))^(2))/(2|m_(1) - m_(2)|)

If sqrt(1 -x^2) + sqrt(1-y^2) = a(x-y), show that, (dy)/(dx) = sqrtfrac(1-y^2)(1-x^2)

Show that the area of the triangle formed by the straight lines y = m_(1) x + c_(1) , y = m_(2) x + c_(2) and x = 0 is (1)/(2)(c_(1)-c_(2))^(2)/(|m_(1)-m_(2)|) sq . Units .

If sqrt(1-x^(2))+sqrt(1-y^(2))=a(x-y) , show that, (dy)/(dx)=(sqrt(1-y^(2)))/(sqrt(1-x^(2))) .

Area of the parallelogram formed by the lines y=mx,y=mx+1,y=nx and y= nx and y=nx +1 equals

The locus of point of intersection of the lines y+mx=sqrt(a^2m^2+b^2) and my-x=sqrt(a^2+b^2m^2) is

If sqrt(1-x^2)+sqrt(1-y^2)=a(x-y) ,show that dy/dx=sqrt((1-y^2)/(1-x^2))

If the ratio of A.M. of two numbers x and y to their G.M. is p : q, show that, x : y = (p + sqrt(p^(2) - q^(2))) : (p- sqrt(p^(2) - q^(2)))

Show that the integer next above (sqrt(3)+1)^(2m) contains 2^(m+1) as a factor.

If y="tan"^(-1) (sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2))) show that, (dy)/(dx)=(x)/(sqrt(1-x^(4)))

CHHAYA PUBLICATION-MISCELLANEOUS EXAMPLES-COORDINATE GEOMETRY (TWO DIMENSIONAL COORDINATE GEOMETRY)
  1. Prove analytically that the bisectors of the interior angles of a tria...

    Text Solution

    |

  2. If d(1),d(2),d(3) be the distances of a fixed point from the straight ...

    Text Solution

    |

  3. Show that the quadrilateral formed by the four lines y=mx+a sqrt(a+m^(...

    Text Solution

    |

  4. Show that the lines x cos alpha+ y alpha=p, x cos (alpha+ (2pi)/(3)) +...

    Text Solution

    |

  5. 2x-y+4=0 is a diameter of a circle which circumscribes a rectangle ABC...

    Text Solution

    |

  6. ABC is right-angle triangle, right -angled at A. The coordinates of B ...

    Text Solution

    |

  7. The line through A( a cos theta,0) and perpendicular to the x-axis mee...

    Text Solution

    |

  8. P and Q are two point on the line x-y+1=0, if O is the origin and bar...

    Text Solution

    |

  9. O(0,0) and A(4,4) are two given points and B is any point. Find the eq...

    Text Solution

    |

  10. Show that the image of the point (h,k) with respect to the striaight l...

    Text Solution

    |

  11. A point moves so that sum of the squares of its distances from the ve...

    Text Solution

    |

  12. Find the locus of mid points of chords of the cirlce. x^(2)+y^(2)=a^(2...

    Text Solution

    |

  13. A straight line is such that its segment between lines 5x-y-4=0 and 3x...

    Text Solution

    |

  14. A rod of length a unit slides on the x-axis and another rod of length ...

    Text Solution

    |

  15. A circle cuts intercepts of length 2a unit and 2b unit from the x-axis...

    Text Solution

    |

  16. Let x^(2)+y^(2)-4x-2y-11=0 be a fixex circle.A pair of tangents to the...

    Text Solution

    |

  17. The circle x^(2)+y^(2)-4x-4y+4=0 is inscribed in a triangle which has ...

    Text Solution

    |

  18. Find the equation of the circle passing through the point (2,0) and to...

    Text Solution

    |

  19. Tangents PQ and PR are drawn from the point (alpha, beta) to the circl...

    Text Solution

    |

  20. Let S-=x^(2)+y^(2)+2gx+2fy+c=0 be a given circle. Find the of the foo...

    Text Solution

    |