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 slope of the tangent line to the curve x+y=xy at the point (2,2) is

Find the points on the hyperbola 2x^(2)3y^(2)=6 at which the slope of the tangent line is -1.

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) .

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

A line L passing through the focus of the parabola (y-2)^(2)=4(x+1) intersects the two distinct point. If m be the slope of the line I,, then

If the tangent drawn to the hyperbola 4y^2=x^2+1 intersect the co-ordinate axes at the distinct points A and B, then the locus of the mid-point of AB 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.

Statement -1 : The lines y = pm b/a xx are known as the asymptotes of the hyperbola x^(2)/a^(2) - y^(2)/b^(2) - 1 = 0 . because Statement -2 : Asymptotes touch the curye at any real point .

Two tangents are drawn to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 such that product of their slope is c^(2) the locus of the point of intersection is