Home
Class 12
MATHS
The tangent at a point p to the reactang...

The tangent at a point p to the reactangular hyperbola `xy=c^(2)` meets the lines `x-y=0, x+y=0` at Q and `R, Delta_(1)` is the area of the `DeltaOQR`, where O is the origin. The normal at p meets the X-axis at M and Y -axis at N. If `Delta_(2)` is the area of the `DeltaOMN`, show that `Delta_(2)` varies inversely as the square of `Delta_(1)`.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS ENGLISH|Exercise EXAMPLE|6 Videos

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS ENGLISH|Exercise SINGLE OPTION CORRECT TYPE QUESTIONS|9 Videos

  • DIFFERENTIATION

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 10|4 Videos

  • ELLIPSE

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|27 Videos

Similar Questions

Explore conceptually related problems

If the normal to the rectangular hyperbola x^(2) - y^(2) = 4 at a point P meets the coordinates axes in Q and R and O is the centre of the hyperbola , then

Tangents at P to rectangular hyperbola xy=2 meets coordinate axes at A and B, then area of triangle OAB (where O is origin) is _____.

Two tangents to the circle x^2 +y^2=4 at the points A and B meet at P(-4,0) , The area of the quadrilateral PAOB , where O is the origin, is

The chord P Q of the rectangular hyperbola x y=a^2 meets the axis of x at A ; C is the midpoint of P Q ; and O is the origin. Then A C O is equilateral (b) isosceles right-angled (d) right isosceles

The tangent to the hyperbola xy=c^2 at the point P intersects the x-axis at T and y- axis at T'.The normal to the hyperbola at P intersects the x-axis at N and the y-axis at N' . The areas of the triangles PNT and PN'T' are Delta and Delta' respectively, then 1/Delta+1/(Delta)' is

A tangent to the hyperbola x^(2)-2y^(2)=4 meets x-axis at P and y-aixs at Q. Lines PR and QR are drawn such that OPRQ is a rectangle (where O is origin).Find the locus of R.

The straight line 2x+3y =24 meets the x-axis at P and the y-axis at Q. The perpendicular bisector of PQ meets the line through (-2,0) parallel to the y-axis at R. Find the area of the DeltaPQR .

If the tangents to the ellipse at M and N meet at R and the normal to the parabola at M meets the x-axis at Q, then the ratio of area of the triangle MQR to area of the quadrilateral MF1NF2 is

For the hyperbola xy = 8 any tangent of it at P meets co-ordinates at Q and R then area of triangle CQR where 'C' is centre of the hyperbola is

The tangent at any point P onthe parabola y^2=4a x intersects the y-axis at Qdot Then tangent to the circumcircle of triangle P Q S(S is the focus) at Q is a line parallel to x-axis y-axis a line parallel to y-axis (d) none of these