Show that the curves `(x^2)/(a^2+lambda_1)+(y^2)/(b^2+lambda_1)=1` and `(x^2)/(a^2+lambda_2)+(y^2)/(b^2+lambda_2)=1` intersect at right angles.

The equation (x^2)/(12-lambda)+(y^2)/(8-lambda)=1 represents

The equation (x^(2))/(10-lambda)+(y^(2))/(6-lambda)=1 represents

The locus of the point of intersection of perpendicular tangents to x^(2)/a^(2) + y^(2)/b^(2) = 1 and (x^(2))/(a^(2) + lambda) + (y^(2))/(b^(2) + lambda) = 1 , is

The equation (x^2)/(2-lambda)+(y^2)/(lambda-5)+1=0 represents an elipse, if

If the lines (x-1)/(1)=(y-3)/(1)=(z-2)/(lambda) and (x-1)/(lambda)=(y-3)/(2)=(z-4)/(1) intersect at a point, then the value of lambda^(2)+4 is equal to

The locus of the point of intersection of the straight lines (x)/(a)+(y)/(b)=lambda and (x)/(a)-(y)/(b)=(1)/(lambda) ( lambda is a variable), is

The differential equation satisfying the curve (x^(2))/(a^(2)+lambda)+(y^(2))/(b^(2)+lambda)=1 when lambda begin arbitary uknowm, is (a) (x+yy_(1))(xy_(1)-y)=(a^(2)-b^(2))y_(1) (b) (x+yy_(1))(xy_(1)-y)=y_(1) ( c ) (x-yy_(1))(xy_(1)+y)(a^(2)-b^(2))y_(1) (d) None of these

Let alpha and beta be the values of x obtained form the equation lambda^(2) (x^(2)-x) + 2lambdax +3 =0 and if lambda_(1),lambda_(2) be the two values of lambda for which alpha and beta are connected by the relation alpha/beta + beta/alpha = 4/3 . then find the value of (lambda_(1)^(2))/(lambda_(2)) + (lambda_(2)^(2))/(lambda_(1)) and (lambda_(1)^(2))/lambda_(2)^(2) + (lambda_(2)^(2))/(lambda_(1)^(2))

If the lines (x-3)/(2)=(y-5)/(2)=(z-4)/(lambda) and (x-2)/(lambda)=(y-6)/(4)=(z-5)/(2) intersect at a point (alpha, beta, gamma) , then the greatest value of lambda is equal to

Consider the equation (x^2)/(a^2+lambda)+(y^2)/(b^2+lambda)=1, where a and b are specified constants and lambda is an arbitrary parameter. Find a differential equation satisfied by it.