The line `P Q` whose equation is `x-y=2` cuts the x-axis at `P ,a n dQ` is (4,2). The line `P Q` is rotated about `P` through `45^0` in the anticlockwise direction. The equation of the line `P Q` in the new position is

If the lines represented by the equation 3y^2-x^2+2sqrt(3)x-3=0 are rotated about the point (sqrt(3),0) through an angle of 15^0 , one in clockwise direction and the other in anticlockwise direction, so that they become perpendicular, then the equation of the pair of lines in the new position is

A straight line passes through P (1,2) and is such that its intercept between the axes is bisected at P. Then the equation of the line is-

The line x/a-y/b=1 cuts the x-axis at P. Find the equation of the line through p and perpendicular to the given line.

The line x =2 y intersects the ellipse (x^(2))/(4) +y^(2) = 1 at the points P and Q . The equation of the circle with pq as diameter is _

If line P Q , where equation is y=2x+k , is a normal to the parabola whose vertex is (-2,3) and the axis parallel to the x-axis with latus rectum equal to 2, then the value of k is

Point P(x, y) is rotated by an angle theta in anticlockwise direction. The new position of point P is Q (x_(1), y_(1)) . If [(x_(1)),(y_(1))]=A[(x),(y)] , then find matrix A.

If the line y=3x+c touches the parabola y^2=12 x at point P , then find the equation of the tangent at point Q where P Q is a focal chord.

If p and q are the roots of the equation x^2+px+q =0, then

If p and q are the two roots of the equation x^2 + px + q = 0 , then find the value of p____

If the roots of a quadratic equation be p+q and p-q, then find the equation.