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

If the straight lines (x-1)/(k)=(y-2)/(2)=(z-3)/(3) and (x-2)/(3)=(y-3)/(k)=(z-1)/(2) intersect at a point, then the integer k is equal to

If the straight line x cos alpha + y sin alpha = p touches the curve (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 then prove that a^(2)cos^(2)alpha+b^(2)sin^(2)alpha= p^(2) .

Let the line (x-2)/(3)=(y-1)/(-5)=(z+2)/(2) lies in the plane x+3y-alphaz+beta=0 . Then, (alpha, beta) equals

The lines x/2=y/1=z/3 and (x-2)/(2)=(y+1)/(1)=(3-z)/(-3) are ….

If the line (x)/(1)=(y)/(2)=(z)/(3) intersects the line 3beta^2x+3(1-2alpha)y+z=3=-(1)/(2){(6alpha^2x+3(1-2beta)y+2z)} then point (alpha, beta, 1) lie on the plane

If the line (x-3)/(2) = (y +2)/(-1) = (z+4)/(3) is in the plane lx + my-z = 9 then l^2 + m^2 = .........

Find the intersection point of (x)/(1)=(y)/(2)=(z)/(2)and2x+y+z=6 .

If x/a + y/b = 2 touches the curve x^n/a^n + y^n/b^n = 2 at the point (alpha, beta), then

If the straight lines (x-1)/(2)=(y+1)/(k)=(z)/(2) and (z+1)/(5)=(y+1)/(2)=(z)/(k) are coplanar, then the plane(s) containing these two lines is/are