Consider a variable plane given by `x/2+y/(beta)+z/(alpha)=1` intersecting the x,y, and x axes at `P,Q,R `respectively then the area of triangle PQR is minimum if `|alpha beta| ` is equal to (A) 4 (B) 3 (C) 2 (D) 1

If plane x + 4y - 2z = 1, x + 7y – 5z = beta, x + 5y + alphaz = 5 intersects in a line (R xx R xx R) then alpha + beta is equal to

If plane x + 4y - 2z = 1, x + 7y – 5z = beta, x + 5y + alphaz = 5 intersects in a line (R xx R xx R) then alpha + beta is equal to

A line makes angles alpha, beta, gamma with X, Y, Z axes respectively. If alpha=beta and gamma=45^(@) , then alpha=

If P(alpha,beta), abgt0 " and the variable line " x/a+y/b=1 " is draw through the given point " p(alpha,beta) , then the least area of triangle formed by this line and the coordinate axes is

If alpha beta gt 0, ab gt 0 and the variable line (x)/(a), (y)/(b)=1 is drawn through the given point P(alpha, beta) , then the least area of the triangle formed by this line and the co-ordinate axes is :

If the normals to the parabola y^(2)=4ax at P meets the curve again at Q and if PQ and the normal at Q make angle alpha and beta respectively,with the x-axis,then tan alpha(tan alpha+tan beta) has the value equal to 0 (b) -2( c) -(1)/(2)(d)-1

A circle with centre (3alpha, 3beta) and of variable radius cuts the rectangular hyperbola x^(2)-y^(2)=9a^(2) at the points P, Q, S, R . Prove that the locus of the centroid of triangle PQR is (x-2alpha)^(2)-(y-2beta)^(2)=a^(2) .