Home
Class 12
MATHS
Prove that if the axes be turned through...

Prove that if the axes be turned through `(pi)/(4)` the equation `x^(2)-y^(2)=a^(2)` is transformed to the form `xy = lambda`. Find the value of `lambda`.

Text Solution

Verified by Experts

The correct Answer is:
`lambda = - (a^(2))/(2)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Transform the equation x^(2)+y^(2)=ax into polar form.

Show that if the axes be turned through 7(1^(@))/(2) , the equation sqrt(3)x^(2)+(sqrt(3)-1)xy-y^(2)=0 become free of xy in its new form.

Find the angle through which the axes may be turned so that the equation Ax+By+C=0 may reduce to the form x = constant, and determine the value of this constant.

The transformed equation of r^(2)cos^(2)theta = a^(2)cos 2theta to cartesian form is (x^(2)+y^(2))x^(2)=a^(2)lambda , then value of lambda is

The equation 4xy-3x^(2)=a^(2) become when the axes are turned through an angle tan^(-1)2 is

If x + y + z =a and the minimum value of a/x+a/y+a/z is 81^lambda , then the value of lambda is

Consider the equation of a pair of straight lines as x^2-3xy+lambday^2+3x-5y+2=0 The value of lambda is

If the points A(-1, 3, 2), B(-4, 2, -2) and C(5, 5, lambda ) are collinear then find the value of lambda .

If (-2,7) is the highest point on the graph of y =-2x^2-4ax +lambda , then lambda equals

The equation ax^2+4xy+y^2+ax+3y+2=0 represents a parabola, then find the value of a.