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`

If the straight line (x-1)/3=(y-2)/2=(z-3)/2 intersect the curve ax^(2) + by^(2) = 1, z = 0 find the value of 49a + 4b.

The line (x-2)/(3)=(y+1)/(2)=(z-1)/(-1) intersects the curve x^2+y^2=r^2, z=0 , then

The line (x-2)/(3)=(y+1)/(2)=(z-1)/(-1) intersects the curve xy=c^2, z=0, if c is equal to

The line (x-2)/(3)=(y+1)/(2)=(z-1)/(-1) intersects the curve xy=c^2, z=0, if c is equal to

Consider the following statements : 1. Equations ax+by+cz+d=0a'x+b'y+c'z+d'=0 represent a straigth line. 2. Equation of the form (x-alpha)/l=(y-beta)/m=(z-gamma)/n represent a straight line passing through the point (alpha,beta,gamma) and having direction ratio proportional to l,m,n. Which of the statements given above is/are correct?

If the line (x-2)/(3)=(y+1)/(5)=(z-2)/(2) lies in the plane alpha x+2y+z-beta=0 then (alpha, beta) equals