Statement 1 : Every line which cuts the hyperbola `x^2/4-y^2/16=1` at two distinct points has slope lying in `(-2,2)dot` Statement 2 : The slope of the tangents of a hyperbola lies in `(-oo,-2)uu(2,oo)dot`

The slopes of the tangents drawn form (0,2) to the hyperbola 5x^(2)-y^(2)=5 is

Show that the line y= 2x -4 is a tangent to the hyperbola x^2/16-y^2/48=1 . Find its point of contact.

Find the equation of normal to the hyperbola 3x^2-y^2=1 having slope 1/3dot

Find the equation of normal to the hyperbola 3x^2-y^2=1 having slope 1/3

Statement- 1 : Tangents drawn from the point (2,-1) to the hyperbola x^(2)-4y^(2)=4 are at right angle. Statement- 2 : The locus of the point of intersection of perpendicular tangents to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 is the circle x^(2)+y^(2)=a^(2)-b^(2) .

The equation of the tangent to the hyperbola 4y^(2)=x^(2)-1 at the point (1,0) , is

Statement 1 : The equations of tangents to the hyperbola 2x^2-3y^2=6 which is parallel to the line y=3x+4 are y=3x-5 and y=3x+5. Statement 2 : For a given slope, two parallel tangents can be drawn to the hyperbola.

If m_1, m_2, are slopes of the tangens to the hyperbola x^(2)//25-y^(2)//16=1 which pass through the point (6, 2) then

A tangent to the hyperbola x^(2)/4 - y^(2)/1 = 1 meets ellipse x^(2) + 4y^(2) = 4 in two distinct points . Then the locus of midpoint of this chord is

Tangents drawn from a point on the circle x^2+y^2=9 to the hyperbola x^2/25-y^2/16=1, then tangents are at angle