The line x cos `alpha + y sin alpha =p` is tangent to the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1.`if

The condition that the line x cos alpha + y sin alpha =p to be a tangent to the hyperbola x^(2)//a^(2) -y^(2)//b^(2) =1 is

If the line y cos alpha = x sin alpha +a cos alpha be a tangent to the circle x^(2)+y^(2)=a^(2) , then

if the line x- 2y = 12 is tangent to the ellipse (x^(2))/(b^(2))+(y^(2))/(b^(2))=1 at the point (3,(-9)/(2)) then the length of the latusrectum of the ellipse is

If x cos alpha +y sin alpha = 4 is tangent to (x^(2))/(25) +(y^(2))/(9) =1 , then the value of alpha is

The locus of poles of tangents to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 with respect to concentric ellipse (x^(2))/(alpha^(2))+(y^(2))/(beta^(2))=1 is

The locus of a point P(alpha, beta) moving under the condtion that the line y=alphax+beta is a tangent to the hyperbola (x^(2))/(1)-(y^(2))/(b^(2))=1 is a conic, with eccentricity equal to

The line y=x+rho (p is parameter) cuts the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 at P and Q, then prove that mid point of PQ lies on a^(2)y=-b^(2)x .

If the line x cosalpha + y sin alpha = P touches the curve 4x^3=27ay^2 , then P/a=

Find the condition that the line x cos alpha+y sin alpha=p may touch the curve ((x)/(a))^(m)+((y)/(b))^(m)=1

Verify , whether the line y=2x + 1 is a tangent to the ellipse 3x^(2) + 2y^(2) = 6.