Tangents are drawn to the hyperbola `3x^2-2y^2=25` from the point `(0,5/2)dot` Find their equations.

Tangents are drawn to the hyperbola 4x^(2)-y^(2)=36 at the points P and Q . If these tangents intersect at the point T(0,3) and the area (in sq units) of Delta TPQ is a sqrt(5) then a=

From points on the circle x^2+y^2=a^2 tangents are drawn to the hyperbola x^2-y^2=a^2 . Then, the locus of mid-points of the chord of contact of tangents is:

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.

(i) Find the equation of tangent to curve y=3x^(2) +4x +5 at (0,5) (ii) Find the equation of tangent and normal to the curve x^(2) +3xy+y^(2) =5 at point (1,1) on it (iii) Find the equation of tangent and normal to the curve x=(2at^(2))/(1+t^(2)) ,y=(2at^(2))/(1+t^(2)) at the point for which t =(1)/(2) (iv) Find the equation of tangent to the curve ={underset(0" "x=0)(x^(2) sin 1//x)" "underset(x=0)(xne0)" at "(0,0)

Find the equation of tangents drawn to the parabola y=x^(2)-3x+2 from the point (1,-1)

From a point P, tangents are drawn to the hyperbola 2xy = a^(2) . If the chord of contact of these tangents touches the rectangular hyperbola x^(2) - y^(2) = a^(2) , prove that the locus of P is the conjugate hyperbola of the second hyperbola.