Coordinate Geometry - Mathematics Previous Year Questions

If the tangent at a point \(\left( {4\cos \phi ,{{16} \over {\sqrt {11} }}\sin \phi } \right)\) to the ellipse \(16{x^2} + 11{y^2} = 256\) is also a tangent to \({x^2} + {y^2} - 2x = 15\), then \(\phi\) equsls

If x = 9 is the chord of contact of the hyperbola x² \(-\) y² = 9, then the equation of the corresponding pair of tangent is

If the straight line \(y = mx + c\) touches the parabola \({y^2} - 4ax + 4{a^3} = 0\), then c is

If a tangent to the circle \(x^2+y^2=1\) intersect the co-ordinate axes at distinct points \(P\) and \(Q\), then the locus of the mid-point of \(P Q\) is

Tangents are drawn to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ at points where it is intersected by the line $l x+m y+n=0$. The point of intersection of tangents at these points is