Tangents

Equation of the common tangent touching the circle $(x-3)^2+y^2=9$ and the parabola $y^2=4x$ above the $x$-axis is

Find the point at which, the tangent to the curve $y=\sqrt{4x-3}-1$ as its slope $\frac{2}{3}$

The condition that the line lx + my + n = 0 becomes a tangent to the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$ , is

If $3x + 4y + k = 0$ is a tangent to the hyperbola ,$9x^{2}-16y^{2}=144$ then the value of $K$ is

The equation of the tangent at any point of the curve $x=acos2t$, $y=2\sqrt{2}a sint$ with $m$ as its slope is

The equation of the tangent line to the curve y = 2x sin x at the point (π/2, π), is