Prove that a line which passes through the point `(alpha, beta, gamma)` and intersects the curve `y=0, z^2=4ax` lies on the surface `(bz-gammay)^2=4a(beta-y)(betax-alphay)`

Find the the image of the point (alpha, beta, gamma) with respect to the plane 2x+y+z=6 .

Find the direction cosine of a line passing through origin and the point (alpha, beta, gamma)

Find the equation of the line which passes thorugh the point P(alpha, beta, gamma) and is parallel to the line a_1x+b_1y+c_1z+d_1=0, a_2x+b_2y+c_2z+d_2=0

Find the equation of the circle which passes through the points (2,3)(4,2) and the centre lies on the straight line y-4x+3=0.

The equations of the line through the point (alpha, beta, gamma) and equally inclined to the axes are (A) x-alpha=y-beta=z-gamma (B) (x-1)/alpha=(y-1)/beta=(z-1)/gamma (C) x/alpha=y/beta=z/gamma (D) none of these

If the straight line (x-alpha)/(l)=(y-beta)/(m)=(z-gamma)/(n) intersect the curve ax^2+by^2=1, z=0, then prove that a(alphan-gammal)^2+b(betan-gammam)^2=n^2

The centre of the circule passing through the points of intersection of the curves (2x+3y+4)(3x+2y-1)=0 and xy=0 is

Find the equation of a line passing through the intersection of the lines x+3y=4 and 2x-y=1 and (0,0) lies on this line.

A straight line passes through the point (alpha,beta) and this point bisects the portion of the line intercepted between the axes. Show that the equation of the straight line is x/(2alpha)+y/(2beta)=1.

If the curve y=ax^(2)+bx+c passes through the point (1, 2) and the line y = x touches it at the origin, then