If the line `2x+sqrt6y=2` touches the hyperbola `x^2-2y^2=4`, then the point of contact is

If the line 3 x +4y =sqrt7 touches the ellipse 3x^2 +4y^2 = 1, then the point of contact is

Prove that the line 5x+12y=9 touches the hyperbola x^(2)-9y^(2)=9 and find the point of contact.

The values of m for which the lines y = mx + 2 sqrt5 touches the hyperbola 16 x^(2) - 9y^(2) = 144 are the roots of x^(2) - (a+b) x-4 = 0 then the value of (a+b) is

Tangents which are parrallel to the line 2x+y+8=0 are drawn to hyperbola x^(2)-y^(2)=3 . The points of contact of these tangents is/are

The line x - y + 2 = 0 touches the parabola y^2 = 8x at the point

Show that the line x + y + 1=0 touches the hyperbola x^(2)/16 -y^(2)/15 = 1 and find the co-ordinates of the point of contact.

Statement 1 : If from any point P(x_1, y_1) on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=-1 , tangents are drawn to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1, then the corresponding chord of contact lies on an other branch of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=-1 Statement 2 : From any point outside the hyperbola, two tangents can be drawn to the hyperbola.

If the chord of contact of tangents from a point P to the parabola y^2=4a x touches the parabola x^2=4b y , then find the locus of Pdot

In a hyperbola, the portion of the tangent intercepted between the asymptotes is bisected at the point of contact. Consider a hyperbola whose center is at the origin. A line x+y=2 touches this hyperbola at P(1,1) and intersects the asymptotes at A and B such that AB = 6sqrt2 units. The equation of the tangent to the hyperbola at (-1, 7//2) is