The number of values of $c$ such that line $y = cx + c$, $c \in R$ touches the curve $\frac{{{x^2}}}{4} + \frac{{{y^2}}}{1} = 1$ is

The co-ordinates of the foci of the ellipse $3{x^2} + 4{y^2} - 12x - 8y + 4 = 0$ are

The locus of the point of intersection of the perpendicular tangents to the ellipse $\frac{{{x^2}}}{9} + \frac{{{y^2}}}{4} = 1$ is

In a triangle $A B C$ with fixed base $B C$, the vertex $A$ moves such that $\cos B+\cos C=4 \sin ^2 \frac{A}{2} .$ If $a, b$ and $c$ denote the lengths of the sides of the triangle opposite to the angles $A, B$ and $C$, respectively, then

$(A)$ $b+c=4 a$

$(B)$ $b+c=2 a$

$(C)$ locus of point $A$ is an ellipse

$(D)$ locus of point $A$ is a pair of straight lines

Let $P(2,2)$ be a point on an ellipse whose foci are $(5,2)$ and $(2,6)$, then eccentricity of ellipse is 

If tangents are drawn to the ellipse $x^2 + 2y^2 = 2$ at all points on the ellipse other than its four vertices than the mid points of the tangents intercepted between the coordinate axes lie on the curve