Write down the foci of the elipse `(x^2)/1 + (y^2)/2 =1`.

The foci of a hyperbola coincide with the foci of the ellipse (x^(2))/(25)+(y^(2))/(9)=1 , find the equation of hyperbola if ecentricity is 2.

the equation of the circle passing through the foci of the ellipse (x^(2))/(16)+(y^(2))/(9)=1 and having centre at (0,3) is

If the foci of the ellipse (x^2)/(16)+(y^2)/(b^2)=1 and the hyperbola (x^2)/(144)-(y^2)/(81)=1/(25) coincide, then find the value b^2

Write down direction cosines of the line (1-x)/1=(y-2)/1=(z-3)/1 .

Let d be the perpendicular distance from the centre of the ellipse x^2/a^2+y^2/b^2=1 to the tangent drawn at a point P on the ellipse. If F_1 & F_2 are the two foci of the ellipse, then show the (PF_1-PF_2)^2=4a^2(1-b^2/d^2) .

Find the equation of the tangent to the ellipse (x^2)/a^2+(y^2)/(b^2) = 1 at (x_1y_1)

Let P be a variable point on the ellipse x^(2)/25 + y^(2)/16 = 1 with foci at S and S'. If A be the area of triangle PSS' then the maximum value of A, is

Write down the adjoint of the matrix [(2,-1),(4,3)]