If the tangent to the parabola `y^(2)-4x` at a point `(alpha,beta).(beta>0)` is also a tangent to the ellipse,`(x^(2))/(4)+(y^(2))/(3)=1` then `alpha` is equal to:

Let L be a tangent line to the parabola y^(2)=4x - 20 at (6, 2). If L is also a tangent to the ellipse (x^(2))/(2)+(y^(2))/(b)=1 , then the value of b is equal to :

If tangent of y^(2)=x at (alpha,beta), where beta>0 is also a tangent of ellipse x^(2)+2y^(2)=1 then value of alpha is

Let a line L : 2x + y = k, k gt 0 be a tangent to the hyperbola x^(2) - y^(2) = 3 . If L is also a tangent to the parabola y^(2) = alpha x , then alpha is equal to

If alpha and beta are the roots of x^(2)+4x+6=0 and N=1/((alpha)/(beta)+(beta)/(alpha)) then N=

The equation of the common tangents of the parabolas y^(2)=4x and an ellipse (x^(2))/(4)+(y^(2))/(3)=1 are

If alpha-beta= constant,then the locus of the point of intersection of tangents at P(a cos alpha,b sin alpha) and Q(a cos beta,b sin beta) to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 is a circle (b) a straight line an ellipse (d) a parabola

Ifchord ofcontact ofthe tangents drawn from the point (alpha,beta) to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 touches the circle x^(2)+y^(2)=c^(2), then the locus of the point